Rovers recorded a first win of the season in Premier League 2 courtesy of two first half goals from Jacob Davenport and Jack Evans, who was also sent off in the game.
Both strikes came early in the encounter before Matthew Virtue pulled one back in the second half.
But Rovers held on, despite Evans' late sending off and a missed penalty from Dan Butterworth to get off the mark in the league with the three point haul.
First team pair Ryan Nyambe and Davenport were both named in the starting XI by Damien Johnson, with Nyambe appearing for the first time since limping off against Nottingham Forest at the end of September.
Davenport, who appeared against Brighton & Hove Albion and Blackpool last week, was hoping to get 90 minutes under his belt against the Reds.
A strong start from Rovers saw captain Joe Grayson's bouncing free kick held well by Kamil Grabara, before the Liverpool stopper denied Neco Williams from scoring an own goal inside the opening four minutes.
But a minute later Rovers took the lead and it came via Davenport, who unleashed a terrific strike into the corner from all of 25 yards.
Things got better for the hosts just 12 minutes later as a Nyambe cross was flicked on by Okera Simmonds and there was Jack Evans to tap home for his second goal in his last two games.
The visitors searched for a response and midway through the half Liam Millar just missed out on getting on the end of Rafael Camacho's cross-shot.
At the other end, a nicely floated pass from Charley Doyle set Butterworth free, but the attacker could only fire wide from an acute angle.
With half time approaching, and with the Reds pushing Johnson's charges back, Millar headed over from a couple of yards out before the impressive Adam Lewis curled just wide of the target from the edge of the box.
But Rovers went in with the advantage by being clinical in front of goal.
After the break, Joe Nuttall had a great chance to add to the tally but he could only glance a header wide after Evans' excellent cross from the left.
Just after the hour, Lewis saw his left-footed free kick crack the crossbar as the Reds continued to push Rovers back.
But a moment later and they did find a route back into the game through captain Virtue. Ollie Byrne produced an excellent stop to flick Camacho's drive onto the bar, but Virtue was there to nod home from a yard out to give the Reds hope.
Rovers were made to see out the final five minutes with 10 men after Evans was shown a second yellow card for hauling down Bobby Adekanye, and Lewis hit the outside of the post with the resulting free kick.
In a nervy last few minutes, Rovers sprung a counter attack, which eventually led to Butterworth being taken down in the box.
The striker dusted himself down, but saw a giant Grabara in his way to tip away from danger.
And the Liverpool goalkeeper wasn't done. With the last chance of the clash, the 'keeper went forward, but headed over an inviting Lewis free kick.
That result gets Rovers off the mark with a first win of the season in Premier League 2, and they are next in action on Saturday away at Manchester City.
Rovers Under-23s: Byrne, Nyambe (Buckley, 65), Evans, C. Doyle, Carter, Grayson (c), Lyons, Davenport, Nuttall, Butterworth, Simmonds (Mols, 57).
Unused substitutes: Eastham, Vale, Candlin.
Goals: Davenport, 5, Evans, 17
Booked: C. Doyle, 53, Evans, 60, Nuttall, 70, Carter, 77
Sent off: Evans, 85
Liverpool Under-23s: Grabara, Williams, Lewis, Johnston, Garcia, Chirivella, Adekanye, Virtue (c), Millar (McAuley, 71), Jones, Camacho.
Unused substitutes: McKenzie-Lyle, Masterson, Christie-Davies, Gallacher.
Goal: Virtue, 63
Booked: Williams, 74
Referee: Garreth Rhodes