Liverpool claimed their first victory since being confirmed as Premier League champions, while Aston Villa's survival hopes took another knock.
The Reds had been embarrassed by Manchester City at the start of their lap of honour last week, and looked on course for another red face on their return to Anfield.
But after 71 largely forgettable minutes, Sadio Mane crashed a winner off the underside of the crossbar. Substitute Curtis Jones celebrated his new contract with a late doubler - his first Premier League goal.
The victory means that City's record points tally of 100 from two seasons ago is still in sight for the Reds - with the three points taking them to 89 points.
Read more on mirror.co.uk