The Dons' Derek Young had been denied by a fine Allan McGregor save during an even first half.
And Randolph held Andrew Considine's header after Derek Young sent the ball back into the box following a corner.
Aberdeen also made two changes, with Diamond and Derek Young starting in place of Rory McArdle and Nick Blackman.
Derek Young's replacement Paton then headed into the arms of Esson, who immediately sent the ball upfield to put the Dons under pressure.
Baur grabbed his second of the evening just after the interval, but Aberdeen battled back and Derek Young reduced the deficit after 56 minutes.
Fit-again Zander Diamond was handed his first start since the opening day of the season, with Derek Young and Davide Grassi dropping to the bench.
Aberdeen responded to a awkward onslaught by making a double substitution after 70 minutes, with Derek Young and Richard Foster coming on for Maguire and Jeffrey De Visscher.
The Dons were forced into an early switch when Cato Guntveit, only just back from injury, was taken off with a knock to be replaced by Derek Young after 17 minutes.
Aberdeen enjoyed a large amount of possession in the early stages and MacLean carved out an opening for Derek Young after 12 minutes, but he fired wide from the edge of the area.
Derek Young fired wildly over the bar before Mark Ferry was guilty of spurning an even better opening at the other end when he failed to apply the finishing touch to Tade's enticing centre.
It was the home support's turn to be incensed when Thomson blew his whistle for a head knock suffered by Derek Young as Barry Ferguson continued the play by slotting the ball into the net from 22 yards.
Hibs' striker Derek Riordan was named young player of the year after a tremendous season in which he has helped his team to the brink of Uefa Cup qualification.
BBC: SPORT | Football | Scottish Premier | Hartson and Ricksen share award
Late in 2006, young guitarist Derek Trucks went into a studio with piano master McCoy Tyner to record "Afro Blue, " so JazzSet opens with an introduction from The Derek Trucks Band with the same song.
Clowe, also acquired at the trade deadline, will be an unrestricted free agent, and young forwards Derek Stepan, Carl Hagelin, Mats Zuccarello, along with key defensemen Moore and Ryan McDonagh are heading into restricted free agency.
But since the young actor in question was named Derek Jacobi, I'm grudgingly forced to admit that posterity has amply vindicated my mother's verdict.
Hibs defender Derek Collins was still able to deliver a slide-rule pass to Miller but the young Hibs forward hesitated and Main blocked.
Derek Bok, a former president of Harvard University, complained in a book published in 1993 that the brightest young students were no longer choosing medicine or the social sciences, let alone academic life: they were going into business.
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