Miller and Fraser Fyvie threatened to put Aberdeen back into the lead before Hearts' Ismael Bouzid's header was superbly saved by Jamie Langfield.
The visitors started brightly and David Obua showed poise in the box to control Craig Thomson's cross before having a shot deflected wide. Minutes later, Driver played a one-two with Lee Wallace and crossed to David Witteveen at the near-post but the Austrian could only find the side-netting as he took the shot on the run.
Aberdeen were given the chance to apply some pressure on the Hearts defence from Charlie Mulgrew's flighted free-kick but Andrew Considine could not keep his header down as he rose above the chasing pack.
Witteveen's glancing header from Thomson's corner flashed across Langfield's goal before Obua's wild effort sailed into the stand.
Some forceful Dons attacking eventually led to a shooting opportunity for Michael Paton but the midfielder could not get a hold of his shot, allowing Janos Balogh to claim comfortably.
Obua's angled drive failed to trouble Langfield before the home side made the breakthrough. Paton raced onto Mulgrew's pass down the left channel and his driven cross was flapped by Balogh, allowing Miller to arrive at the back post and head into an empty net.
The Dons could have doubled their lead early in the second half when Fyvie's corner was cleared to the edge of the box where Peter Pawlett was waiting but the midfielder blazed his shot high and wide. Fyvie advanced down the left as Aberdeen tried to catch Hearts on the break but, after beating Ismael Bouzid, the youngster fired over from a tight angle.
Hearts levelled when substitute Christian Nade held the ball up well and created the space for Driver on the left to slide a shot beyond the advancing Langfield.
Aberdeen went back on the offensive and Balogh punched Fyvie's inswinging corner over before Miller could not divert Chris Maguire's free-kick into the net.
Miller then skilfully escaped the challenge of Wallace before seeing his shot blocked by Balogh. The Dons continued to press and Fyvie's goal-bound volley was headed clear by Goncalves.
Bouzid almost gave Hearts the lead for the first time when he connected with Thomson's corner but the alert Langfield beat the ball away from under the crossbar.
As the match entered the closing stages, Langfield failed to claim a Thomson corner and Obua had two efforts blocked - one an open goal when he could only head yards wide - before Jose Goncalves' shot was cleared on the line and Nade eventually fired over amid some frantic Aberdeen defending.
Csaba Laszlo really needs to sort out Obua's dismal finishing, but there's not much he can do with Witteveen, who has shown again he is not worthy of a place in the Hearts team.