It was Terry McPhillips side's first defeat of the season in a game in which they started strongly but ended with a whimper.
The first half saw the visitors enjoy plenty of possession, keeping Bolton penned back but without ever creating any clear cut chances.
Bolton had offered little as an attacking force for the first part of the half, but they took the lead in stunning circumstances at the midway point when Tom Youngs smashed home on the half volley from outside the area.
Rovers' response was to again gain plenty of possession but the lack of a cutting-edge saw them trail at the break.
Any hopes that Rovers would kick on in the second half were quickly extinguished when the home side grabbed a second on 55 minutes.
It came courtesy of a Rovers error as Bradley Mason gifted possession and Elliott Newby made no mistake.
Another error lead to Bolton's third on 78 minutes as Robbie Cotton played a square ball across the area which allowed Youngs to pounce for his second of the game to secure the points for the home side.
"I was quite happy with the way we played in the first half," said coach McPhillips. "We had lots of the ball and were in and around their goal creating a few half chances.
"But in the second half we just didn't get going, it was really disappointing because we weren't competitive and that isn't like us.
"We missed Deniz Pero as he was down to play but was ill the night before.
"We got the lads back in on Monday and to be fair to them they put in a good shift in training and now we are very much looking forward to getting back on track away at Everton on Saturday."
ROVERS: Raya, Anderson (sub Rittenberg 80 mins), Beesley, Brown, Mason, Thompson, Cotton, Wassi (sub Bauress 70 mins), Preston (sub Laverty 70 mins), Boland.
Subs not used: Humphreys, Harris.