Boston United extracted three more precious third division points from a match dominated by gale force conditions which did neither side any real favours.
In the end, it was a solitary goal from debutante Danny Thomas which settled the issue and produced a result which fired Boston into mid-table and left Rovers still facing a relegation battle.
In the blustery conditions Boston went close after just 16 seconds when a raking drive by David Noble was held by keeper Kevin Miller.
In the eighth minute Boston went even closer when new signing Thomas crossed from the left and Graeme Jones crashed a header against the post with the ball dropping straight into Miller's arms.
Bristol's first response of note came when a long range drive by Graham Hyde flew straight at keeper Paul Bastock.
Boston kept up their attacking tempo and Miller was again a busy man when clutching a shot by Steve Melson and then on 32 minutes when he dived bravely at the feet of Jones who was looking to finish off a cross by Stuart Douglas.
Boston finally got their reward when Thomas fired them ahead from a 38th minute free kick low to the left of an unsighted Miller after Melson had been tripped by Rob Quinn.
Bristol became a more threatening force after the break assisted by the strong wind at their backs and almost drew level on 51 minutes when Christian Edwards headed just too high from a Gary Twigg corner.
Boston still had bright moments despite losing the services of Jones through injury and in the 64th minute substitute Lee Thompson wasted an opportunity when blazing high over the bar from a Thomas free kick.
Rovers went close again in the 68th minute when Bastock had to stretch to claim possession as Paul Tait and Junior Agogo tried to meet a Twigg cross.
Back at the other end, Douglas met a Thomas free kick in the 71st minute but headed too high.
Bristol answered with another attacking burst and when the ball broke to Adam Barrett his rasping 25 yard drive flew inches over the home bar. Then a curling free kick by Twigg flashed just wide.
In the 83rd minute, Thomas burst clear again for Boston and forced Miller into a sprawling save with a powerful drive. Moments later, Douglas got into a shooting position but again found Miller well placed to save.
Deep into stoppage time, Rovers almost equalised when Tait found space, but shot straight at Bastock.
Boston boss Steve Evans said: "It could have been comfortable from our point of view. The gales made life difficult, but even when we were against the wind I felt we ensured Bristol didn't have many chances." Rovers caretaker-manager Phil Bater said: "The wind was a bit of a nightmare. It was a match of two poor teams and we were the worst of the pair. We have found goals hard to come by all season and this was the case again here."