Moeen Ali returned figures of 4/92 while Leach finished with 4/71 as England overcame some staunch resistance from Kusal Mendis, Roshen Silva and later Malinda Pushpakumara to bowl the hosts out for 284 and seal the three-match series 3-0 at the SSC in Colombo.
Resuming on 53/4 chasing a daunting 327 runs to win, Sri Lanka lost the wicket of nightwatchman Laksan Sandakan (7) early with Leach inducing a thin edge that was taken by Ben Stokes easily at first slip.
Mendis and Silva then grafted it out and made sure they did not give the visitors any easy wickets. England on their part looked insipid too. While Leach bowled some unplayable deliveries, both Moeen And Adil Rashid were not able to get the same bite from the surface which was on show late last evening.
There were too many boundary balls on offer and both batsmen made sure they took full toll of it. Mendis was the more aggressive of the duo as he brought up his fifty - his seventh in Tests - in just 54 balls with Silva playing the perfect foil, bringing his nimble footwork to good effect on more occasion than one.
England's frustration was visible after Ben Stokes was officially warned for bowling three bouncers in an over as Sri Lanka moved to lunch comfortably placed at 164/5 scoring 111 runs in the opening session for the loss of just one wicket.
The first few overs after the break also did not have much success for England, with both batsmen able to rotate strike at every given chance and collecting the odd boundary as well. With England looking flat a moment of brilliance was needed by someone and Leach provided that - not with the ball though, but on the field.
In the 58th over of the innings, Silva nudged a googly off Rashid wide of fine leg. He hared down the wicket calling for two and assuming the throw would be at his end made his ground. But Leach, showing amazing game awareness rushed to pick up the ball and in one swift motion pinned the wickets down at the non-striker's end where Mendis - not expecting the throw - was found well short for 86. The sixth wicket partnership between Mendis and Silva ended on 102 and the visitors suddenly found their mojo again.
Leach then got rid of Dickwella for a run-a-ball 19, caught at forward short leg before Moeen got into the act picking up the wicket of Dilruwan Perera (5) who presented Keaton Jennings with his sixth catch of the Test - equalling the record of most catches in a match for England.
Silva meanwhile reached a half-century - his second of the series - but once Moeen had him lbw for 65, England sensed a series whitewash with Sri Lanka still needing 101 more to win.
Pushpakumara, batting at No.11 and Suranga Lakmal, managed to give the visitors a mighty scare with the duo adding 58 runs for the final wicket. Pushpakumara slammed six fours and a six in his 42-ball 40 to force the game into the final session despite the extra half an hour.
However, any plans of a miracle were laid to rest by Leach in the first over after tea when he trapped Lakmal for 11 to claim his fourth wicket and give England a remarkable win. Root became the first England captain since Nasser Hussain in 2001 to win a Test series in Sri Lanka.
Jonny Bairstow was named Player of the Match for his century in the first innings while Ben Foakes was awarded Player of the Series.
adil rashidEngland cricket teamJack LeachJoe Rootkusal mendisMalinda PushpakumaraMoeen Aliroshen silvasri lanka cricket teamSri Lanka vs Englandsri lanka vs england 2018
First Published: November 26, 2018, 4:24 PM IST