'Mass' struck a lovely goal to open the scoring in the 23rd minute, a precise, curling shot from 25 yards as Town had the better of the first half at Brunton Park.
However, the hosts turned up the pressure in the second half and finally got their rewards in the last minute as Mark Beck headed home.
David Symington then hit the winner for the home side in extra time. Massimo played the full 120 minutes.
It hasn't been the best week for Town, as they were beaten 6-0 by Blackpool in the Championship on Saturday. Massimo played 65 minutes at Bloomfield Road.
In League One, Ryan Fredericks remained an unused substitute as Brentford beat Crewe 5-1 on Saturday.
Simon Dawkins continues to impress for San Jose Earthquakes in the MLS. He scored twice as the Earthquakes beat Colorado Rapids 4-1 to remain top of the Western Division.
In Greece's Super League, Bongani Khumalo played 90 minutes as PAOK opened their 2012-13 campaign with a 1-0 win against Panthrakikos on Sunday.