With a 2-0 lead in the bank, victory at Pallekele would wrap things up with a game to spare, while the hosts were hoping their score of 273 for seven would be enough to keep the contest alive heading to Colombo.
Dasun Shanaka’s career-best 66 – including five sixes – and important knocks from Niroshan Dickwella (52) and Thisara Perera (44) helped Sri Lanka post a competitive total on a sluggish pitch.
Leg-spinner Adil Rashid was England’s most economical bowler with one for 36 from his allocation, while Moeen Ali took out two of the top three.
Olly Stone, who has made a bright start to his career in his maiden series, struggled to make an impact this time and was taken for 50 from seven wicketless overs.
The tourists were without opener Jonny Bairstow, their top-scoring batsman in 2018, due to an ankle injury sustained during a game of football. Alex Hales took his place at the top of the order.