England's win keeps their chances alive in the seven-match series, with the visitors now trailing 2-3 against Sri Lanka with two matches still to play.
Root's 104 not out laid the foundation for England's win, and earned him man of the match.
Taylor was omitted for the first three games, and has been determined to prove the selectors wrong ever since, scoring 90 in the last game.
His robust knock of 68 this time around included five fours and a six.
Sri Lanka opened with two spinners when England began the chase on Thursday, after rain forced the visitors to abandon starting their innings on Wednesday night.
Sachithra Senanayake, the comeback man for Sri Lanka, struck in his fourth ball to dismiss the dangerous Moeen Ali and followed up later by trapping England captain Alistair Cook lbw to leave England 35-2.
Senanayake had been raced into the side for Thursday's barely 24 hours after the International Cricket Council lifted its ban on the off-spinner over an illegal bowling action.
But after the two wickets fell, Root and Taylor took charge, with delectable strokeplay to leave the spinners reeling.
After Taylor's dismissal, Root added 86 for the fourth wicket with Ravi Bopara to take England closer.
Partnering with Root, Josh Butler scored two runs in the first ball of the final over to hand England the match.
The sixth international will be played in Pallekele on Saturday. The series gives both teams a chance to build for the World Cup to be held in Australia and New Zealand in February-March.

Latest News from Sports News Desk