Leaders Celtic's game at Partick Thistle was called off due to a waterlogged pitch early on Thursday, presenting Derek McInnes' men with the chance to reach the summit.
And it was an opportunity they grabbed with both hands, as David Goodwillie gave the home side a sixth-minute lead with an overhead kick at Pittodrie.
The result - Aberdeen's sixth win in a row - lifts them a point clear of Celtic, who now have a game in hand.
Stuart Armstrong's fortuitous opener set the tone for the rest of the match, with United going in 4-1 up at the interval.
The home side's relentless onslaught continued into the second half with goals from Jaroslaw Fojut and Charlie Telfer, before Luka Tankulic netted a late consolation.
Following their disappointing defeat to Kilmarnock last time out, the Premiership's fourth-placed side responded in emphatic fashion courtesy of five different goalscorers.
Having ended their seven-match winless run against Hamilton on Saturday, Kilmarnock made it back-to-back victories with a 2-1 triumph at St Mirren.
Defeat for the hosts leaves them one point clear of the relegation position currently occupied by Ross County, who were comfortably beaten 3-1 at home by Inverness Caledonian Thistle.
