Chasing a target of 220 on a sluggish pitch, Root struck 75 off 90 balls while captain Harry Brook scored 42 and Ben Duckett 39 as the visitors won with more than three overs to spare.
The hosts would have felt they still had a sniff in the contest when reducing England to 189-5 with Root and Brook dismissed.
Former skipper Jos Buttler (33 not out) however made sure the tourists will play a third and deciding match in the series.
Sri Lanka has earlier laboured to a total of 219 all out as the home team's batteras could not get going after winning the toss and opting to bat.
Home skipper Charith Asalanka struck 45 and Dhananjaya de Silva 40 but none cold go on and get a big score that was required.
England spinner Adil Rashid took 2-34 in his 10 overs while Root and seamer Jamie Overton also grabbed two scalps.
The third and deciding ODI of the series will take place in Colombo Tuesday with the teams then also playing three T20I matches.
Kusal Mendis' calm, unbeaten 93 set the platform as Sri Lanka beat England by 19 runs in the first one-day international in Colombo on Thursday, punishing another late collapse from the tourists.
England were forced into a late change ahead of the opening ODI against Sri Lanka in Colombo after off-spin-bowling allrounder Will Jacks was ruled out having fallen ill overnight.
England white-ball captain Harry Brook admits he needs to "regain the trust of the players" following an altercation with a nightclub bouncer in New Zealand in October.
Former England fast bowler Stuart Broad has come to the defence of head coach Brendon McCullum and captain Ben Stokes, saying the current Test team does not have a drinking culture.
