Emma Hayes’ side had taken an early lead as Fran Kirby got them up and running from the spot, but two second-half penalties from Katie Stengel turned the match on its head and gave newly-promoted Liverpool a massive win to start their campaign.
It ended the Blues’ 13-game unbeaten streak, while Liverpool celebrated their return to the top-flight in front of a record 3,006 fans at Prenton Park.
Former Blues defender Flaherty got her new side off to a disastrous start, mistiming her clearance and instead making contact with Reiten to concede a penalty inside the first minute.
Kirby stepped up to the spot and sent Rachael Laws the wrong way to convert inside three minutes, her 29th goal in her last 31 starts for the Blues.
Emma Koivisto had a chance to level soon after when Chelsea keeper Zecira Musovic failed to hold onto a Ceri Holland effort, but the Finnish defender sent her effort over the bar from the rebound.
The defending champions dominated throughout the opening exchanges with Lauren James, who earned her first England cap earlier this month, looking especially bright down the right wing.
They looked to double their advantage at the 20-minute mark when Kirby sent a long ball over the top to Kerr, who fired past Laws from 18 yards but her volleyed effort was immediately ruled offside.
Liverpool levelled it up when Flaherty’s flick-on from a throw-in caught Millie Bright’s arm and was called for handball and Stengel coolly converted for her first WSL goal.
Three minutes from time, Stengel broke down the right and into the area, pursued by Buchanan who brought her down with a sliding tackle to set up Stengel, who kept her nerve from the spot to complete the comeback.
Earlier on Sunday, Rachel Daly enjoyed a dream debut for Aston Villa, scoring twice as they beat Manchester City 4-3 in a thrilling encounter.
Tottenham also got their season up and running with victory, beating Leicester 2-1. Drew Spence made her debut after leaving Chelsea in the summer, scoring at both ends of the pitch though thankfully for her the own goal did not cost her new side.
Lisa Evans’ goal was enough to give West Ham a narrow 1-0 win over Everton, and her former club Arsenal sit top of the table after the opening week of action.
They face Tottenham next weekend in a north London derby at the Emirates, with more than 45,000 tickets already sold for the fixture.
Additional reporting by PA Sport.