Bolton strolled into the FA Cup fourth round after a clinical performance.
Davies set Bolton on their way to victory
The Premiership side took only eight minutes to score, Kevin Davies coolly volleying into the corner from Stelios Giannakopoulos' clever, chipped pass.
Donny almost equalised but Ian Walker superbly saved Mark McCammon's header, and Andranik Teymourian made them pay when he drove home into the top corner.
Idan Tal followed up his own shot to score Bolton's third before Teymourian slid in his second after the break.
Playing the first FA Cup match in their new Keepmoat Stadium, Dons never managed to look anything other than a side which plays two divisions beneath Bolton.
Nervous in defence and hesitant on the ball, the hosts failed to rise to their new surroundings and the challenge of a potential giant-killing act.
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Instead they were grateful that keeper Ben Smith was able to make fine stops from Teymourian, in particular, and a host of Bolton players, who began to form a queue to try their luck.
Unfortunately for Smith, he could do little to keep out any of Bolton's efforts - starting with Davies' sweetly-struck opener.
The same was true of Teymourian's rising drive as Bolton extended their lead, just moments after the Iranian had been denied by Smith.
And Smith must have felt everything was against him when he proved equal to Tal's shot only for the Bolton midfielder to convert the rebound.
It seemed the goal would be disallowed as the assistant referee flagged for offside against two Bolton players, but referee Dermot Gallagher overruled.
Bolton added a fourth shortly after the break when Davies squared the ball for the on-rushing Teymourian to collect, avoid a lunging challenge and then calmly stroke into the bottom corner.
From then on, Bolton selected cruise control and allowed Doncaster a little more time and space on the ball.
But whereas the visitors' finishing had been clinical, Dons failed to take advantage of a couple of promising moments despite Paul Heffernan's best efforts to snatch a consolation.
Doncaster manager Sean O'Driscoll:
"We were brave in what we tried to do, but they were bigger, stronger and faster. I can't complain.
"At four-nil up they had 10 men behind the ball working hard. We can take a lot from learning how they have got where they've got. They were excellent.
"If we can learn our lessons and progress from having played against them, we'll be a better side for it."
Bolton boss Sam Allardyce:
"It was a tricky tie but we have made it look easy.
"We made a lot of changes but the fluidity of the side was still good and that was very pleasing.
"I was pleased that we played in their new stadium because it would have been a bit daunting for some of our players if it had been at their old ground."
Doncaster: Smith, Paul Green, Lockwood (Stephen Roberts 83), Lee, O'Connor, Coppinger, Wilson, Stock, Forte (Guy 70), McCammon (Price 60), Heffernan.
Subs Not Used: Dyer, Thornton.
Bolton: Walker, Hunt, Faye, Meite (Augustyn 83), Gardner, Teymourian, Tal, Fortune (Smith 51), Giannakopoulos, Davies (Anelka 73), Vaz Te.
Subs Not Used: Al Habsi, Speed.
Goals: Davies 8, Teymourian 22, Tal 33, Teymourian 49.
Ref: D Gallagher (Oxfordshire).