Leach came in as night-watchman with one over left to negotiate, which he safely did, playing out a maiden to see England through to the close.
Root, who scored 35 and three in the first Test, was bowled by Pushpakumara in the 18th over for 14 and Rory Burns (43) soon followed as England slumped to 89 for four before lunch.
"Rooty (captain Joe Root) has been massive in the dressing room saying "don't worry about making mistakes" and we're just trying to go out with a positive mindset. We feel if we can put pressure on them with our batting, get a good total, then we can win".
"At one point we felt like we could have a lead, or be level, so we're a little bit disappointed with that".
According to worldwide cricket rules an umpire can dock five runs if he feels the batsman ran a short run deliberately.
Dananjaya frustrated England's spinners before falling to Moeen Ali leg before for 31.
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Suranga Lakmal and Silva added 28 runs for the last wicket. "They tried a lot of things but we managed to counter them", Karunaratne said.
'They should have it within them to bat a decent number of overs and then it's over to Sri Lanka.
"As we were walking back Burnsy [Rory Burns] said to me 'I've been waiting a long time to open the batting for England and you've done it too quickly".
"The next couple of days are going to be exciting for spin bowlers and batters are going to be on their toes", predicted Curran.
WICKET: Leach falls early on Day 3.
Sri Lanka face a hard task to stay alive in the three-test series, having lost spinner Rangana Herath to retirement and skipper Dinesh Chandimal to a groin injury.
De Silva kept his calm after losing Karunaratne and raised his fifty with a boundary off Stokes.