Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
Raheem Sterling scored a hat-trick as champions Manchester City made a convincing start to their title defence with a 5-0 win over West Ham United.
A round-up of all the international friendlies played on Tuesday
News of all that's transpired on and off the football field
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News of all that's transpired on and off the football field
An insatiable Lionel Messi scored for the eighth game in a row in all competitions as La Liga champions Barcelona saw off a gutsy Girona side 2-0 to go five points clear at the top of the standings.
News of all that's transpired on and off the football field
Holders Spain suffered their first defeat in qualifying for a major tournament in eight years when Miroslav Stoch nodded a late goal to earn Slovakia a shock 2-1 victory in Euro 2016 Group C on Thursday.