Jurgen Klopp’s champions-elect were short of their fluent best in windy conditions at Carrow Road but returned immediately to winning ways after their winter break.
Liverpool have gone 43 top-flight matches unbeaten, just six matches behind Arsenal’s record of 49 games in 2003-04 and are sprinting towards their first league title for 30 years.
“You’re probably bored of me saying it but we’re one step closer, it’s just about focusing on the next game,” he added. ‘We’ve just got to keep doing what we’ve been doing all season, never change that.”
The result leaves Daniel Farke’s Norwich rooted to the bottom of the table, six points behind 19th-placed Watford. They look set for an immediate return to the Championship despite their battling performance.
Klopp brought back midfielder Naby Keita for his first start in a Premier League match since December and Mane was on the bench as Liverpool started with confidence.
Liverpool forward Roberto Firmino was particularly impressive, producing an exquisite piece of skill to control a long Jordan Henderson pass before the ball was stolen off his toes as he shaped to shoot.
But despite a few scary moments, Farke’s men kept Liverpool quiet and came close to snatching the lead themselves.
Lukas Rupp got in behind the Liverpool defence and controlled a long ball over the top. He opted to pass to his left to Teemu Pukki but Alisson Becker produced a superb save, clawing the ball away at the feet of the Finnish striker.
– Mane breaks deadlock –
Pukki had a late chance to equalise but shot straight at Alisson as Liverpool held on for their 25th win in 26 Premier League matches.
Defending champions Manchester City, reeling from a potential two-season European ban for breaching fair play rules, are in second place in the table but have no chance of winning a third straight title.