A wonderful goal from Dunn in the first half and a stinker of an own goal in the second saw Rovers win on the road for the first time in eleven attempts.
Rovers went into this Reebok clash nursing an away record to forget with ten consecutive defeats, but those memories were banished by a much improved display which fully warranted the three points.
Both sides had chances to opening the scoring in the early exchanges, David Dunn saw a lob cleared off the line whilst Matty Taylor wasted a great opportunity for the home side.
But a 30 second spell just past half hour saw Rovers ride their luck and then take full advantage when Taylor saw his free-kick deflect off Nelsen and crash onto the crossbar. Paul Robinson's throw to Franco Di Santo set Rovers on their away, he found Jason Roberts who then teed the ball fo David Dunn who curled a superb effort into the far corner despite Jaaskelainen's best efforts.
The second half saw Rovers twice thwarted by Gavin McCann as the visitors upped the ante, the pressure eventually telling when a hopeful ball forward by Brett Emerton was headed into the back of his own net by Sam Ricketts after a mix up.
Substitute Lars Jacobsen cleared well off his own line as Bolton threatened a late scare, but Rovers were full value for the victory.
After Saturday's news that manager Sam Allardyce would miss the next three games due to a required heart operation no doubt he was watching on with great pride as his side won in his absense.
Before the game Sam Allardyce had picked the team, making just the one change from the side that started against Portsmouth a fortnight ago. As goal hero Jason Roberts returning to the starting line-up as Morten Gamst Pedersen made way.
It was a bright opening from Rovers, David Dunn volleying wide after just four minutes, then Franco Di Santo saw a shot deflected wide of goal.
But at the other end Rovers were then fortunate when a Gavin McCann centre found Matt Taylor at the back post, but his first touch allowed Gaël Givet to make a vital block.
David Dunn then went close to opening the scoring when after getting the better of Gary Cahill in the area, but his lob was cleared off the line by O'Brien
But past the half hour and a chance at either end within the space of 30 seconds would Rovers gain the upper hand and the lead.
It started with a Bolton free-kick 35 yards out. Taylor struck it goalwards where Robinson looked to have it covered until the ball deflected in the opposite direction off the boot of Nelsen. Rovers and their fantastic support held their collective breaths as they ball flew towards goal, but they breathed a sigh of relief as it crashed off the crossbar.
In an instant the ball was in the hands of Paul Robinson and he wasted little time in throwing it out to Franco Di Santo on the left, he took the ball from inside his own half to the edge of the Bolton area before finding partner Jason Roberts who held off his man long enough to feed David Dunn.
The Rovers number 8 clipped a delightful ball into the opposite top corner of the net that Jussi Jaaskelainen got his fingertips to the ball but it was a strike of such quality that he couldn't keep out.
It was Dunn's sixth goal of the season.
But Rovers were then forced into a rearguard reshuffle when Gaël Givet couldn't continue after picking up a kick to the thigh. Lars Jacobsen coming on to replace the Frenchman with Pascal Chimbonda switching to left back.
At the end of the first half Bolton had chances to get back on level terms, Robinson clawed a Taylor centre away from under his own bar, before the former Portsmouth midfielder headed wide from the resulting corner kick.
Rovers attacked Bolton straight from restart, El-Hadji Diouf almost scoring on his return to the Reebok, but Gavin McCann made the block in front of goal to deny.
Roared on by a fantastic following, Rovers had Bolton rocking, Emerton fed Dunn who slipped a great ball onto Di Santo, but the young striker was denied by Jaaskelainen.
Then from a corner it was Gavin McCann who thwarted Rovers once more, Ryan Nelsen winning the first header, Jason Roberts nodding it on but the Bolton midfielder cleared from under his own bar.
Then Steven Nzonzi blazed wide when well placed as Rovers continued to press for a second.
And so the pressure told, when on 73 minutes when Rovers added their second in fortunate circumstances.
Brett Emerton sent a ball forward in search of Benni McCarthy but Sam Ricketts and Jaaskelainen were on the wrong wavelength as the Bolton defender headed back to where his 'keeper had been only to look on in horror as the ball rolled into the empty net.
With a two goal advantage Rovers were able to knock the ball around with more composure and assurance, Brett Emerton going close to a third only to be denied by a low save by the Bolton goalkeeper.
On 88 minutes Bolton had their best chance of the game. A long ball forward was missed by both centre halves, Ivan Klasnic took the ball around Paul Robinson but Lars Jacobsen was in the right place at the right time to slide in and clear from inside the six yard box.
"Big Sam's blue and white army" chanted the visiting supporters as Rovers saw out the four additional minutes without incident. No doubt somewhere the absent Sam Allardyce was watching on with a smile on his face.
BOLTON: Jaaskelainen, K. Davies (c), Ricketts, O'Brien, Muamba, Cahill, Samuel, McCann (sub M. Davies 69 mins), Elmander (sub Klasnić 66 mins), Gardner (sub Lee 69 mins), Taylor.
Subs not used: Al Habsi (GK), Basham, Knight, Steinsson.
ROVERS: Robinson, Chimbonda, Samba, Nelsen (c), Givet (sub Jacobsen 35 mins), Emerton, Dunn (sub Grella 85 mins), Nzonzi, Diouf, Roberts, Di Santo (sub McCarthy 71 mins).
Subs not used: Brown (GK), Andrews, Kalinić, Salgado.
Booked: Muamba, Taylor, Klasnić (Bolton), Dunn (Rovers).