Rovers had battled back from behind when skipper Rob Jones had scored a carbon copy of MacKenzie’s header from a corner on the hour.
The visitors had snatched the lead in the 17th minute when new signing Steven Davies celebrated his debut with a simple goal from close range.
But Rovers showed their mettle in the second half and were rewarded with Jones’ leveller before being cruelly hit by two late goals.
MacKenzie struck in the 87th minute before Tom Ince grabbed a third for good measure deep into injury time.
Blackpool had the better of the earlier skirmishes as both sides took some time to settle at the start.
They had the first chance in the ninth minute following a left-wing cross from Bobby Grant but teenage full-back James Husband did well to nick the ball off Tom Ince’s toes.
But the visitors had a lucky escape moments later when Chris Brown headed inches wide from Mark Duffy’s right-wing cross with Matt Gilks beaten.
Ross Turnbull was almost caught unawares when he had to parry a shot from Davies at the near post after the striker had tried his luck from a difficult angle.
But the resulting corner led to Tangerines making the breakthrough in the 17th minute.
Angel Martinez’s shot from the edge of the box was partially saved by Turnbull who did remarkably well to recover and parry Kirk Broadfoot’s follow up shot.
But the ball ran straight to the feet of Davies who had a simple tap in from close range.
David Cotterill had a 20 yard free kick saved by Gilks when Rovers tried to hit back and then Duffy blasted a chance over the top in the 35th minute.
Chances went begging again from Rovers when Brown had an effort saved and Richie Wellens headed over the bar from close range on the stroke of half time.
Rovers applied pressure at the start of the second half and were rewarded when they equalised on the hour.
Cotterill delivered a splendid corner and Jones rose high to send a powerful header into the back of the net.
Play went off the boil for a spell with both teams becoming bogged down in midfield before the dramatic late finale.
Ince missed a golden opportunity to restore Blackpool’s lead in the 84th minute when he rolled the ball wide of the mark after being gifted an opening by defender Paul Quinn.
But the visitors’ persistence was rewarded in the 87th minute when MacKenzie headed home unchallenged from Ince’s corner.
Doncaster piled everyone forward in a bid to fight back and Ince cashed in when he fired a low curving shot into the unguarded net from 40 yards after Turnbull had gone up for a Rovers’ corner and could not get back in time to prevent the goal.