Jackie McNamara's side's have become the form team in the country in recent weeks and carried that on despite the visitors equalising in the first half through Jamie Hamill's penalty after Brian Graham had given the hosts an early lead at Tannadice.
Graham netted his second goal of the afternoon with a header early in the second half before late goals from Gary Mackay-Steven and John Rankin rounded things off in the closing stages for a 4-1 win.
It was harsh on Hearts, who had battled hard - but United look capable of giving anyone a game on this kind of form.
Kris Boyd netted the winner for Kilmarnock as the Ayrshire side picked up their first away league win of the season - a 2-1 victory over Ross County.
With both teams toiling towards the bottom of the table, the three points lifted Killie above Saturday's hosts. Chris Johnston and Boyd netted to counter a reply from Stuart Kettlewell.
St Johnstone welcomed Sir Alex Ferguson back to the club but saw two other former employees steal the show as Aberdeen claimed a 2-0 win.
Ferguson was at the game to mark the 50th anniversary of his hat-trick in a 3-2 victory for St Johnstone over Rangers at Ibrox, but it was the club he is more famously associated with that were celebrating as former Saints manager Derek McInnes tasted victory in his first competitive return to McDiarmid Park.
And it was Peter Pawlett, who spent the first half of last season on loan at the Perth club, who did the damage with an excellent long-range strike in the 17th minute.
Another player facing his old club, St Johnstone substitute Rory Fallon, made a similarly dramatic but less positive impact after being sent off for an elbow on Michael Hector two minutes after coming on.
That put the game well beyond St Johnstone and Niall McGinn further stretched Aberdeen's lead with a stunning strike five minutes from time to move the Dons into fourth, five points and two places above the Saints.
John Hughes first game as Inverness boss ended in stalemate as the Highlanders were held to a 0-0 draw by St Mirren in Paisley.
The Buddies enjoyed the better chances in the first half but the closest they came was when Steven Thompson - making his 100th appearance for the club he supported as a boy - struck Dean Brill's upright after 25 minutes.
Second place Caley Thistle also hit the woodwork when Marley Watkins headed against a post with 20 minutes left but Saints survived on that occasion to extend their unbeaten streak to five games, ensuring they stay just a point behind Hibernian in seventh place in the Scottish Premiership table on 16 points.
James Collins struck a dramatic late equaliser to rescue a point for Terry Butcher against Partick in his first home match in charge of Hibernian.
The Republic of Ireland Under-21 international, who has endured a frustrating spell with Hibs since arriving from Swindon in close season, lashed home from close range to secure a 1-1 draw and break the hearts of the resolute visitors.
Hibs have still only won two league matches at Easter Road in the whole of 2013, and looked destined for defeat when Kris Doolan gave the Glasgow outfit a shock second-half lead in the capital.