Falkirk, by contrast, find themselves in a relegation dogfight and after giving away a soft penalty and later missing a sitter the signs are not encouraging for the Bairns.
United certainly began like a team with European ambitions as they dominated the early exchanges. Central defender Lee Wilkie started as he meant to go on by winning a header at the back post which Lee Bullen had to clear inside the six-yard area.
Striker Steve Lovell then passed up two half-chances during rare Falkirk counter-attacks and midfielder Scott Arfield shot wildly over, but the visitors were still in control and after Craig Conway's shot was blocked they went ahead in the 28th minute.
Full-back Tom Scobbie clearly handled the ball and Conway stepped up to replace Francisco Sandaza, who had missed against Hearts on Saturday, to squeeze the penalty pass keeper Danny Mallo.
Michael Higdon made an unconvincing appeal for a home penalty minutes later but United might have gone two-up after 37 minutes when Mallo flapped at a cross from Paul Caddis before Sandaza failed to capitalise on the goalkeeper's mistake.
At the other end, a poor clearance by United keeper Lukasz Zaluska left Higdon with an open goal to aim at, but for some reason he instead opted to pass to Lovell.
Falkirk improved after the break and Bullen tested Zaluska with a downward header before Lovell somehow directed another header wide with the whole stadium expecting to see the net bulge.
United also had their chances to kill Falkirk off but Wilkie sent a looping header wide and Caddis nodded the ball straight at Marlow from close range.
Falkirk dominated the closing 20 minutes in terms of territory and possession, but with Wilkie and Darren Dods both immense at the back United held on comfortably.