Liverpool, who are back in the top flight after winning WSL 2 last season, came from behind to claim the stunning victory at Prenton Park.
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It looked as though it would be a routine match for Emma Hayes' side when Fran Kirby put them ahead with a penalty on three minutes.
But the Reds, who are managed by Matt Beard, rallied and levelled midway through the second half through Katie Stengel's spot-kick.
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And the hosts got their second penalty of the match in the 87th minute, Stengel making no mistake as she sent Zecira Musovic the wrong way.
It capped off a thrilling start to the 2022/23 season, which also saw Aston Villa edge to a 4-3 victory over Manchester City.
Arsenal, who missed out on the title by a point last term, kicked off the season with a 4-0 thrashing of Brighton on Friday night.
Elsewhere, Manchester United beat Reading by the same scoreline, while West Ham and Tottenham claimed wins against Everton and Leicester respectively.
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