Diamond slotted home after a quickly-taken free-kick to cancel out Flavio Paixao's second-half header.
Hamilton were left with a strong sense of injustice after being denied a penalty moments earlier when Jim Paterson brought down Dougie Imrie.
David Elebert missed two excellent late chances to win the game for Hamilton, who looked the more impressive team for much of the match, while Aberdeen's ninth game without victory did little for their faltering top-six challenge.
Only 2,030 fans turned out to watch two teams who have struggled in recent weeks, with Hamilton having found the net just three times in 11 games before today.
Both sides started with three up front, though, with Aberdeen bringing in Sone Aluko and Michael Paton and Hamilton swapping Flavio Paixao for the injured James Wesolowski. Hamilton had the better of the early exchanges, with Paixao having a shot held by Jamie Langfield amid a series of corners.
Steven MacLean found room on Aberdeen's right flank but Paton fired well over from his cutback and Hamilton continued to dominate possession.
Brian Easton's cross just evaded Paixao at the far post following a sustained passing move and David van Zanten volleyed wide on the run after Simon Mensing had sent him clear down the right.
Elebert looped a header into the side netting from Easton's floated free-kick and Paixao's shot ended up in the same place after James McArthur had burst into the box.
Mark McLaughlin and Mensing were booked for dissent after the former was penalised for a tug on Paton seconds after his team-mate claimed Paterson had pushed him inside the Aberdeen box.
Charlie Mulgrew curled the 20-yard free-kick towards the top corner but Tomas Cerny leapt to push it away one-handed.
Imrie was too high with a free-kick at the opposite end and van Zanten headed wide from Paixao's deep cross.
Aberdeen created the first opening of the second half when Langfield's huge kick-out allowed MacLean space but there were no takers when he rolled the ball across the six-yard box.
Paton fired a 25-yard strike just past the far post as Aberdeen, now playing 4-4-2, began to enjoy more possession and territory.
Hamilton's top scorer, Mickael Antoine-Curier, replaced van Zanten after missing six matches following knee surgery.
The hosts took the lead in the 62nd minute when Paixao headed home Easton's inswinging corner from inside the six-yard box.
Aberdeen created an immediate chance to reply when Richard Foster cut the ball back for Gary McDonald 15 yards out but Martin Canning threw himself at the midfielder's shot to divert it over. Imrie then stabbed wide after a one-two with Mensing as the game opened up.
Aberdeen boss Mark McGhee brought on Darren Mackie to revert to a three-man strikeforce but Aberdeen escaped a strong penalty claim in the 75th minute when Paterson brought down Imrie after the forward had cut in from the right wing.
Aberdeen were level within 60 seconds when the unmarked Diamond, earlier booked for a strong aerial challenge on Imrie, slotted home MacLean's cutback after a quickly-taken free-kick by Mulgrew.
The Dons soon had another chance but Alex Neil cut out Mackie's square ball as MacLean waited for an open goal.
Hamilton had another penalty claim but Paixao's shout was more ambitious after he was brushed off the ball by Mulgrew, and the Portuguese forward soon fired just over from 18 yards after being set up by Imrie.
Elebert headed just wide after McArthur's measured ball had found him unmarked eight yards out and the defender fluffed another close-range chance in the final seconds.