Daly volleyed home from 18 yards just after the interval to add to Craig Conway’s free-kick in a first half dominated by the hosts.
Scott Robertson headed a simple third to finish off a poor Hearts side, who had Eggert Jonsson sent off.
United, who ended a run of 13 SPL games without a win at Aberdeen last weekend, looked a confident side going forward as they racked up their third victory in eight days.
Robertson controlled midfield and Conway and Willo Flood caused Hearts numerous problems down the wings as Craig Levein’s men sealed back-to-back league wins for the first time since January.
The only consolations for a toothless Hearts outfit were their retention of third spot and Danish striker Mike Tullberg’s second-half debut.
United threatened from the start and Daly went very close after five minutes. The Irish striker, who missed the midweek Co-operative Insurance Cup win over Airdrie because his wife was rushed to the operating theatre following the birth of daughter Sophie, headed Conway’s near-post corner off the bar.
Marian Kello rescued Hearts five minutes later when left-back Lee Wallace let in Sean Dillon, whose attempt to dink the ball over the on-loan Kaunas keeper was blocked.
The backtracking Kello made an equally good save midway through the half when he tipped over Robertson’s backward header following Flood’s driven free-kick.
Hearts had a good spell of possession but their lack of cutting edge was apparent.
United threatened again when Conway aimed a free-kick at Darren Dods in the six-yard box, with Kello unconvincingly challenging to divert the ball over his crossbar.
The home side were making far better use of the flanks and left-winger Conway fired a shot that had Kello scrambling down at his near post.
But the keeper could do nothing about Conway’s 30-yard fee-kick in the 39th minute, which was curled into the top corner.
Hearts created their best chance of the half when Christos Karipidis headed over from six yards as he stretched to reach an Audrius Ksanavicius free-kick.
But United hit the bar again when Morgaro Gomis followed a tidy piece of skill 30 yards out with a powerful strike that bounced over.
Hearts wide man Saulius Mikoliunas got in behind the United defence for the first time following Ksanavicius’ reverse pass just after the restart, but Lee Wilkie was quickly across to block.
And Daly doubled United’s lead in the 50th minute when he chested down Flood’s cross on the edge of the box and volleyed in off the post.
Hearts tried to respond but substitute Christian Nade and Christophe Berra could not direct efforts on target when crosses fell into their path.
Tullberg, who suffered an injury following his summer transfer from Italian side Reggina, came on in the 59th minute in place of Jamie Mole.
But the points were wrapped up two minutes later when the unchallenged Robertson headed Conway’s free-kick past the stranded Kello.
Hearts looked demoralised and another great burst forward by Flood set up Daly on the right side of the box but his shot was straight at the keeper.
Jonsson received his second yellow card from Dougie McDonald in the 74th minute following a body-check on Conway just inside the United half.
Both sides his the woodwork in an otherwise low-key final quarter. Mikoliunas cut inside and fired a 20-yard strike off the post before Conway’s cross came back out off the bar.