Francisco Sandaza gave the visitors the lead after 10 minutes from the penalty spot after having been needlessly fouled by Diamond.
The Dons equalised within twenty seconds of the restart through Scott Severin before David Robertson blasted his side in front once more.
But Diamond made amends for his earlier error by bravely heading his side back level after 72 minutes.
Diamond started in the Aberdeen central defence after recovering from an Achilles injury, while Darren Mackie returned from a hamstring injury to start in attack for the Dons ahead of Tommy Wright.
United made four changes to the side that drew 1-1 with Inverness Caledonian Thistle last weekend. Daniel Grainger, Darren Dods, Warren Feeney and Robertson came in to replace Paul Dixon, Jon Daly and Craig Conway, who dropped to the bench, while Garry Kenneth who missed out completely.
Careless defending from the visitors almost gave the Dons an early lead after six minutes. Mackie pounced on a misplaced Grainger header before feeding Chris Maguire but the young striker's effort went just past the post.
And United had the chance to make the Dons pay for their miss after 10 minutes when Diamond conceded a penalty after bringing Sandaza down in the box.
The Dons defender, who had been limping after an early challenge with Feeney, was shown a yellow card for his needless foul. The United striker dusted himself off before smashing the ball past Jamie Langfield from the spot.
The home supporters were appealing for a penalty of their own after 28 minutes when Mackie fell under pressure from Dods but referee Willie Collum waved away the half-hearted appeals.
Aberdeen continued to search for an equaliser and Lee Miller was unlucky to see his thunderous volley from 25 yards go fizzing over the bar after 33 minutes.
The Dons were dominating proceedings and Lukasz Zaluska was called into action for the first time to deny a Maguire volley after 38 minutes.
Dods was cautioned for a late challenge on Sone Aluko five minutes before half-time. Charlie Mulgrew's curling effort from the resulting free-kick dipped inches over Zaluska's bar.
The Dons came out from the break at full speed and grabbed an equaliser within 20 seconds of the restart. Aluko surged down the left before delivering a tantalising ball into the centre for Mackie who could not connect but Severin was on hand to prod the ball home.
Langfield was called onto make a magnificent save from a Feeney volley after 54 minutes to prevent his side falling behind again.
But United did restore their advantage in sensational fashion moments later. Paul Caddis eased past Mulgrew on the touchline before cutting the ball back for Robertson who smashed the ball in off the upright from the edge of the box.
The home side should have got back on level terms after 63 minutes when Mark Kerr crossed for Miller but the Scotland international could only look on in agony as his header came back off the bar.
The tiring Sandaza was replaced by Craig Conway after 68 minutes.
Aberdeen got a deserved equaliser after 72 minutes thanks to a deadly delivery from Charlie Mulgrew. The former United full-back found Diamond in the area who bravely headed the ball past the stranded Zaluska to restore parity once more.
Mulgrew then had a go himself from a free-kick but his effort sailed harmlessly over the bar.
Craig Levein injected a bit more pace by bringing on Danny Swanson for Robertson after 79 minutes.
Aberdeen pressed for a winner in the closing stages with Maguire and Kerr both going close with long-range efforts.
However the home side could not find a third goal to clinch victory and instead had to settle for a hard-fought point.