The result, in the final FA WASL round of matches before the summer break, also saw the hosts overtake Bristol Academy at to the top of The FA Women’s Super League on goal difference.
Liverpool took the lead after a quarter of an hour; with German winger Rolser converting after Dowie's shot came back off a post.
Birmingham then levelled after 26 minutes following a corner when left-back Kerys Harrop (pictured) hooked the ball home.
Stung by conceding an equaliser, the Reds went on the offensive, as Blues struggled to cope with their crisp passing. Dowie, a constant menace, got clear but was denied by an excellent double-save from Earps. It was a brief reprieve. From the resulting corner, Liverpool left-back Bronze rose highest and emphatically headed home to restore the home team’s lead.
But Birmingham were gaining a foothold in the game and missed a chance to equalise when an unmarked Isobel Christiansen volleyed over. They could not have been any closer on 64 minutes when Potter’s 25-yard shot from outside the box struck both posts before being cleared by the Liverpool defence.
Dowie got the goal her performance deserved to seal the win in the 84th minute, although there was a touch of fortune about it as a Fara Williams shot flicked off her heel.
Rolser got her second of the game two minutes later with a low finish to put further gloss on the victory.
Birmingham manager David Parker felt the scoreline was harsh on his players. “It didn’t reflect the balance of play,” he said. “The width of two posts was the difference between drawing the game and losing it.
"Liverpool’s third goal was a lucky one that flicked off the heel. Those are the fine margins in this league.”
Liverpool Ladies: Laws, Easton, Bronze, Engen, Schroder (Riccio 88), Fors, Holbrook, Da Costa (Omarsdottir 81), Rolser, Williams, Dowie (Fenlon-Billson 91)
Unused substitutes: Gibbons, Chappell, Keryakoplis.
Goals: Rolser 15 & 86, Bronze 37, Dowie 84
Blues Ladies: Earps, Weston, Bassett, Westwood, Harrop, Moore, Potter, Lawley (Haines 82), Christiansen, Linnett (Wilkinson 81), Williams
Unused substitutes: Hourihan, Simpkins, Torkildsen, Ballard, George
Goals: Harrop 26
Referee: M Salisbury