The Bairns more than held their own in a goalless first 45 minutes but conceded twice shortly after the break thanks to Danny Cadamarteri's third goal of the season and David Goodwillie's first.
New signing Kjartan Finnbogason pulled one back on his Falkirk debut but United held on to make it seven points from three games this term.
Former Celtic youth striker Finnbogason, on loan from Norwegian club Sandefjord until January, was allowed to play after international clearance came through on time.
United made four changes from Tuesday's Co-operative Insurance Cup win at Alloa, recalling Nicky Weaver, Andy Webster, Danny Swanson, and Cadamarteri, who recovered from a throat infection.
As they had done in the first half against Hibernian a week earlier, Falkirk set about denying their opponents time and space early on.
United were still bossing possession though, and Robert Olejnik had to be alert to parry Cadamarteri's 13th-minute snapshot, which flicked off Goodwillie.
Paul Dixon was booked two minutes later for bringing down Bairns forward Carl Finnigan as the visitors began to get into the game.
And Finnbogason could have put them in front in the 17th minute when Weaver fumbled a Burton O'Brien corner, but the striker's follow-up was blocked by a combination of Dixon and Webster.
Falkirk were growing in confidence and O'Brien fired narrowly wide from 20 yards after a poor Webster clearance.
United's more creative players were struggling to make an impact but they should have taken a 35th-minute lead when Swanson tricked his way into the box and sent in a shot Olejnik could only parry to Goodwillie.
Finnigan was the hero on the line, blocking his fellow forward's follow-up.
And United finished the first half on top, with Swanson's free-kick deflected over after Scott Robertson was fouled, before Cadamarteri blazed high and wide when well placed.
The restart saw United boss Craig Levein throw on David Robertson for namesake Scott.
The game exploded to life two minutes into the half when Scott Arfield threaded a ball through to Ryan Flynn, who beat a floundering United offside trap but not Weaver, the goalkeeper easily winning their one-on-one contest.
The home side charged down the other end and Brian McLean blocked Goodwillie's shot before Cadamarteri opened the scoring in the 49th minute.
Swanson crossed from the right and Cadamarteri finished left-footed from a tight angle at the back post.
Six minutes later, it was 2-0, Swanson again the provider as Goodwillie stayed onside to fire a low near-post finish past Olejnik.
Just as against Hibs, Falkirk appeared to be paying for their first-half endeavours.
And they suffered an injury scare on the hour when team-mates Olejnik and Thomas Scobbie collided chasing a short O'Brien backpass.
The keeper was soon on his feet but Scobbie was down for two minutes.
He was eventually helped up but substituted as a precaution alongside Jackie McNamara, with Chris Mitchell and Alex MacDonald coming on.
The latter fired a free-kick well over as the shellshocked visitors tried to respond.
With 15 minutes remaining, Bairns boss Eddie May brought on Danijel Marceta for Flynn.
It paid dividends two minutes later, Finnigan's through ball playing Finnbogason into acres of space behind the United defence and the Norwegian kept his cool to round Weaver and score.
Gomis became the second United player booked when he threw the ball away after bringing down O'Brien and Chris Mitchell soon followed suit for Falkirk for deliberate handball.
With seven minutes remaining, Olejnik held Cadamarteri's turn and shot, before United withdrew Goodwillie for Andis Shala and Swanson for Craig Conway.
Falkirk could have levelled in stoppage-time but Marceta's low cross evaded everyone.