The Dons dominated from the outset and were only denied an early opening goal by Scotland goalkeeper Paul Gallacher, who made two fine stops within seconds of each other on the quarter-hour mark.
First he had to show strong hands to smother Sheerin's fine volley from the edge of the area then, even more impressively, dived low to his left to push Steve Tosh's blistering drive round the post for a corner.
Aberdeen's pressure paid off in the 21st minute when they deservedly took the lead. Hinds raced on to McGuire's long ball and, having dragged David McCracken out of position, slipped a low shot across Gallacher's body into the far corner.
United were in disarray and went further behind three minutes later after a piece of woeful defending. They failed to pick up McGuire at a corner and when Scott Morrison's swirling cross reached him on the six-yard line he had the simple task of nodding it home.
Hinds, who has been criticised - not least by his own manager - for his lack of goals, was brimming with confidence as he proved, in the 36th minute, by shooting just wide from David Zdrilic's flick on.
Aberdeen confirmed their superiority by adding a third just before the break. Once again United's defending was poor as Sheerin ran into the box to collect Zdrilic's slightly mis-hit cut-back and roll it into the net.
The Dons started the second half in the same vein as the first and, unfortunately for United boss McCall, so did his defenders. Once again Zdrilic and Hinds combined to set up a chance for the latter, but he could not find the target.
McCall was clearly unhappy with the fare served up by his players and made three changes in the first 20 minutes of the second half. He replaced McLaren, Jim McIntyre and Mark Kerr with Scotland, Billy Dodds and Trinidadian forward Collin Samuel.
Aberdeen continued to push forward in search of more goals and Hinds went close once again, in the 71st minute, with a rasping shot from the edge of the area that smacked off the crossbar with the goalkeeper well beaten.
Zdrilic, too, hit the woodwork three minutes later, with a well-struck free-kick that had Gallacher scrambling. He had the opportunity to snatch the fourth at the death, but missed a simple opportunity from a few yards out.
Their fine afternoon was soured, however, as McGuire was carried off injured right on the final whistle following a clash with Scotland.
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