United made the long trip to the Memorial Stadium looking to bounce back from a disappointing home defeat last weekend which had seen them create chances only to be put to the sword by table toppers Forest Green.
Lukas Jensen was in for his first league start, with Magnus Norman sidelined through injury following the Saturday home fixture.
Also missing with niggles were Rod McDonald, Kelvin Mellor and Joe Riley, with Danny Devine drafted in at right back and Zach Clough recalled into the forward positions alongside Lewis Alessandra and Brennan Dickenson.
Jordan Gibson was back into the match day 18 having got rid of an illness, and the defensive reshuffle included a return to the heart of the back line for Corey Whelan at the expense of Jonathan Dinzeyi.
The Gas had the first attack of the day when Evans picked up a misplaced pass in midfield. He spread it to Anderson, who dropped a shoulder before dinking a cross to the back stick. Saunders challenged but Devine did well to get in the way.
A corner for the hosts on five minutes saw Brown trot over to deliver. It was low, and Clough cleared on the spin to release Dickenson. His early crossfield pass was latched onto by Alessandra, who had raced into the area. Devine helped, but his cross was cut out.
Space opened up for Evans unexpectedly when a long kick came his way, but he slipped as he was urged to shoot by the crowd. It skewed off his boot and curled well wide.
A foul by Feeney on Saunders over by the corner flag earned him a yellow card, and Evans sent the dead ball in at head height to the six-yard box. Taylor got a head to it but it went high and over the bar.
Harries was next to go in the book when he got hold of Young's shirt as the forward upped a gear, and that gave Clough the chance to test the resolve. He sent it long and Hoole got there ahead of Feeney.
A Devine clip on Brown as he went on a break brought another floruish of the yellow from referee Charles Breakspear, and Evans opted for power from what was a tight angle. Guy followed the sweep of the ball to guide it away.
Chances were hard to come by and Clough had a shot from distance charged down as he bent a run to try to make a gap.
The away side had a great opportunity to open their account when Alessandra controlled well from a fizzed pass from deep. The ball broke to Clough, but his fierce drive was quickly blocked. Dickenson was onto it but his snapshot was parried by the hands of the alert James Belshaw.
But it was Rovers who took the lead when an incisive move caught the black shirts flat-footed. Three passes from back to front released Evans and he jinked past Devine before thundering an unstoppable shot into the bottom corner.
Dickenson beat the offside trap as United looked to respond but his cut back went behind Young, and Anderton was able to clear.
Carlisle had a real chance to level things up on 48 minutes when a huge kick forward from Jensen was flicked on by Dickenson. Belshaw was off his line, and Clough went for the lob when he got there first. The keeper threw his hands up to make the save.
It was a good spell from the visitors as Mellish and Alessandra tried to pick a way through, and they came again when a half clearance from an Armer cross ricocheted to Guy. He fed it to Dickenson, and a whisked pass across the face of the target had Clough and Devine interested. They couldn't get the touch and Coutts intervened.
Dickenson then beat his man on the left flank before whipping one in, but yet again it was a boot from the Pirates that got there first.
Feeney headed over from a Clough corner just past the hour, but he was at a tight angle and it was always going to be difficult.
Another Clough corner went begging when it skimmed off Dickenson, as he leaped high to try to make it count inside the danger area.
The corners kept coming and Clough bent another into the ruck after a Guy pass had been diverted away. The clearance came to Guy, but his 25-yarder was straight at Belshaw.
Carlisle looked to show attacking intent and excellent skill from Gibson saw him lose his man on the halfway line but he was twice prevented from shooting as he reached the edge of the area.
Having enjoyed the bulk of the second half possession the Cumbrians were undone for a second time with four minutes left to play when substitute Luke Thomas turned a scrappy piece of tackling into a decisive run. He reached the byline, pulled it back, and fellow replacement Sam Nicholson was there to stroke the weighted pass into the back of the nets.
Abrahams nodded just past the upright when he got on the end of a Clough free kick as the clock ticked down, and Gibson swirled one past the post from distance.
And it got worse for United in time added on when Saunders suddenly found himself with just Jensen to beat. He kept his cool and smashed it into the roof of the net.
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Goals
Bristol Rovers - Evans (35), Nicholson (87), Saunders (90+5)
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Bookings
Bristol Rovers - Harries (23), Saunders (76), Thomas (88), Whelan (90)
Carlisle United - Feeney (16), Devine (26), Alessandra (38), Armer (60), Guy (61), Mellish (74)
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Teams
Bristol Rovers - Belshaw, Collins (Nicholson 78), Coutts (c), Taylor, Anderson (Thomas 68), Evans, Saunders, Harries, Whelan, Hoole, Brown (Anderton 37). Subs - Ward (gk), Westbrooke, Martinez, Pitman.
Carlisle United - Jensen, Devine, Feeney, Whelan, Armer (Charters 72), Dickenson, Guy (c), Mellish, Alessandra (Gibson 53), Young (Abrahams 63), Clough. Subs - Breeze (gk), Dinzeyi, Mampala, Toure.
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Match officials
Referee - Charles Breakspear
Assistant Referee 1 - Stephen Brown
Assistant Referee 2 - Michael Begley
Fourth Official - Andrew Laver
Observer - Rodger Gifford
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Attendance - 6,302 (292)