Train connections? QUICK!

You really don't need to book Milan to Varenna in advance since it is a regionale. You can just buy that from a machine when you get to Milan.

When you get to Milan buy the ticket to Varenna.

Thank you! Was hoping to speed up the trip since I've heard about how accurate the rail system is. I doubt I'd be able to get off the train and buy a ticket for a train departing 5 minutes later and be able to board the train. Plus I prefer to have as many tickets in hand prior to trip.

or buy the 14:20 in advance;

If you buy all tickets online, the Regionale ticket for the trip to Varenna should be pre-validated, and good for trips in a four hour window from the listed departure time. Therefore if you miss the 13:20 departure, you can use the same ticket for the next departure. If in doubt, check with the Conductor when you arrive in Milan.

The Freccia trains are usually quite reliable, but there's no guarantee there won't be unexpected delays.

In the worst case scenario, you'd have to buy another ticket to Varenna. It's only a few Euro so not a serious problem.

Five minutes is sort of tight in a station as large as Milan. You have to get to one of the Departure screens, find the train you want on it, get the platform number, and walk to that platform, which may be some distance away. If the regional is originating in Milan, it probably will manage to leave on time.

Thanks everyone! Had no idea about the 4 hour window!

Why not just buy the Milan to Varrena regional train ticket from a kiosk at the Venice train station and then validate it before you board the regional train in Milan? The ticket can be used for any Milan to Varrena regional train that day as it won't be prevalidated (so you must validate it before boarding the regional train).

A bit more information on the ticket. According to the Trenitalia website....

"The ticket purchased online is already validated with the date and time of departure chosen by the customer and has a validity of four hours. Different usage periods may be provided by the individual tariffs and other tariff provisions.
The departure can take place within the validity of the ticket."

If you do happen to be delayed a long time and don't make the four hour window, a ticket is only €6.70 so not a huge amount.

Could you clarify one point in your post? You indicated that your Freccia arrives at Milano Centrale at 13:45. If that's the case you WON'T be able to connect with a 13:20 departure, as that train will have left the station 25 minutes before you arrive. You'll have to book the 14:20 departure which provides a transfer time of 35 minutes (lots of time).

Damn fat fingers! Arrival time is 13:15. Basically have 5 minutes before train to Varenna leaves or wait an hour for next train. Thanks!

You can switch train in Milano C. in 5 minutes only under the most optimistic circumstances - arriving train in perfect time, departing track close to the arriving track. Usually connections in Milan are scheduled for 15 minutes or more.
As suggested, the best thing to do is buying the Milano-Varenna ticket in Venice and validating it at the track. Going down to the ticket office in Milan would take a long time, and online regional tickets have more limitations than ordinary tickets.

You can switch train in Milano C. in 5 minutes only under the most optimistic circumstance

Lachera is right, are you buying on trenitalia.com? I'm quite sure that on the official site the minimum transfer time at Milano Centrale is 15 minutes. If you purchase a shorter connection on a third party site trenitalia won't protect you.

There is free wi-fi on Frecciargento and Frecciarossa trains. If you have a smartphone, when you are halfway between Milan and Venice purchase the regional train ticket using trenitalia's app. You could be able to make it in 5 minutes only if the first train is running exactly on-time.

Sometimes I have made very tight connections (one with a delayed train under 3 minutes in Bologna C.) using the Trenitalia app to know in advance on which tracks we are arriving and departing, so that I could plan the run. Of course, you would need to be familiar with the station layout.

I don't want to be the cold water in your shower, but:
http://www.milanocentrale.it/en/map/#

You might have to hump it from the middle of platform 20, with luggage to platform 4 or lower, in five minutes. You're on a freccia, so assigned car/seats on the incoming, and likely not in 1st, so probably halfway down the platform or more. The regionale departure, you can sit anywhere, so won't have to go to the middle of the platform.

Slow down and enjoy the sites. Milano Centrale is a wonderful/horrible piece of fascist architecture, with great people watching. Take the time, feel oppressed by the building's immensity, and admire the stylish people. And slow roll your way to your departure gate. If it's your first trip to Europe, you might just find the train stations fascinating in their own right. And Milano Centrale, being one of the remaining fascisti pieces of infrastructure around, is interesting in it's own right.

The 17.15 from Udine should arrive at track #14 and the 17.20 to Sondrio leaves from track #4. - But you cannot be 100% sure these will be the track assignments on a given day. - You may get a little advantage by walking to the head of your first train, if possible, but not very practical if you have luggage. - Again, this change of train is possible only under the best circumstances.

It's an out of date reference, but I'm not sure I'd trust OJ Simpson to make that five minute connection, even if it was to a Hertz counter.
https://youtu.be/FA1S9KY78QY

Thanks for the clarification. As lachera and the others have said, it's highly unlikely that you'll be able to make a 5 minute connection. You'd have to know the Binario no. of your next train (which can change and sometimes not posted until shortly before departure), be in the closest coach to the front and at the front of the line in the foyer to disembark from the Freccia train. You'd then have to run at top speed down one platform and up another, while hauling your luggage. Given the crowds at Milano Centrale, that's an impossible scenario. If you happen to be on one of the farthest coaches from the front of the train, the platform will fill up with people disembarking in front of you, which will impede your progress.

I think it would be far wiser to book the 14:20 train. Stop at one of the restaurants and have a coffee or a small meal.

When you are finally on the train to Varenna: make sure you know which stop is the one before Varenna.
The local trains don't stop for long, so you need to be out of your seat and standing by the door with your luggage in order to get off as soon as the train has stopped at Varenna.
I believe the platform is on the left hand side.
We did that, and then couldn't get the door to open!
A handy teenager was on board and he ran up the aisle to help us!
Just made it off in time before it started up again!