Paul Paton, formerly of United, was dismissed for a Falkirk side that collected a further six yellow cards.
Aaron Muirhead's penalty came late and provided the travelling support with brief hope, with United having taken a 2-0 lead through a deflected Sam Stanton effort and a Pavol Safranko header.
As it happened: Dundee United 2-1 Falkirk
The first chance of the match went to Dundee United, arriving from the first of what would be a string of first half corners for the hosts.
Frederic Frans met the ball well but saw it head a yard wide of the left hand post.
Falkirk's first chance came on the quarter of an hour mark, and it was a decent one. Zak Rudden nodded the ball goalwards, with Benjamin Siegrist parrying wide.
The resulting corner saw efforts from Marcus Haber and Aaron Muirhead foiled by Swiss stopper Benjamin Siegrist.
That gave United the wake up call they needed, however, and they took the lead just five minutes later. Sam Stanton's effort took a deflection off of Aaron Muirhead and left Mitchell stranded in the middle of his goal.
Robbie Neilson's side had a couple of half chances as they looked to go in two up, with McMullan and Stanton both firing in weak efforts from in and around the box.
Centre-half Rachid Bouhenna's effort, though, was anything but weak as he lashed a firecracker goalwards from ten yards with Mitchell doing superbly to tip it onto the bar.
Into the second half and the Bairns had clearly been riled up at half-time, coming out and putting in a few poor challenges - with Marcus Haber going into the book for an elbow.
On 53 minutes, it was pretty much game over. Fraser Aird's corner was on the money and, with help from some poor marking and Haber's woeful attempt at clearing the ball, Safranko headed in for 2-0.
Haber, again poor, left the park just over five minutes later to cheers. Surely one of his very last appearances in a Falkirk shirt.
The Canadian departed as part of a double change, but Ray McKinnon's plans were out of the window within seconds of his changes as Paul Paton saw red.
The midfielder, returning to Tannadice, stood on Safranko's hand before headbutting the striker, with referee Steven Kirkland left with no choice but to send him off.
Sammut and Buaben both went into the book, with Aird, man of the match on the day, firing a free-kick just over on 70 minutes.
Craig Curran had a chance for the hosts, with David Mitchell making an impressive double save from the striker and midfielder McMullan.
Falkirk carved out their first chance of the second half on 77 minutes, with Rudden sidefooting a tame effort into the hands of Siegrist from 20 yards.
Mitchell, the Bairns' best player on the day, had another save left to make in the dying minutes - denying Frederic with a stunning dive down to his left.
With the game seemingly fading away, suddenly Dennon Lewis sparked into life. The striker took on all comers, three or four players, before being felled by former Bairn Paul Watson in the box. The referee, who actually slipped during the build-up, pointed to the spot.
Captain Aaron Muirhead, lucky to be on the pitch after a woeful tackle on Billy King, converted.
Even with that goal coming in added time, that wasn't that. Craig Curran shoved substitute Scott Harrison into the hoardings, with the Bairns defender reacting angrily and both being yellow carded.
A ridiculously feisty second half, which the hosts ultimately dominated, ended a goal apiece but that wasn't enough to stop Falkirk falling to a 2-1 defeat.