Root's innings came after the hosts were given a small scare after being reduced to 80-4 by the tourists bowling unit before the Yorkshireman guided his side home with more than 15 overs to spare.
Earlier in the day the Sri Lanka again gave a dismal batting display, being bowled out for just 185 thanks to impressive bowling performances from Chris Woakes and David Willey.
Woakes shines as Sri Lanka struggle with the bat yet again
Having just come off the back of a three match T20 series in which Sri Lanka hit a high score of just 129-7 earlier this month, expectations were not high for their batsman when they were put into bat by Eoin Morgan at the beginning of play.
And things got off to a rather predictable start when the tourists fell to 46-3 inside the first 8.3 overs with Pathum Nissanka and Dasun Shanaka falling to Woakes and Charith Asalanka nicking off to Willey all for scores of under six.
Sri Lanka did mount somewhat of a fightback throughout the middle overs, however, when captain Kusal Perera and Wanindu Hasaranga managed to frustrate the England bowlers and put on a partnership of 99, taking the score to 145-3 by the 28th over.
The Lions' hopes of reaching a score that would really look to test the world champions batting line up quickly began to disintegrate, though, when Hasaranga top edged a short ball from Woakes and was taken superbly by a diving catch from Liam Livingstone at deep backward square leg for a score of 54.
Following this, the lack of experience in the Sri Lanka team began to become badly exposed with them losing their final six wickets for just 40 runs.
Just nine balls after Hasaranga went Arachchige Dhananjaya would fall victim to a wonderful diving catch at slip by Joe Root for only two, nicking off against the superb Woakes who would finish the day with figures of 4-18.
New batsman Ramesh Mendis would also lose his wicket for just one shortly after, before the big wicket of Perera fell in the next over when he was caught on the boundary by Sam Billings off the bowling of Willey for 73, leaving the score on 152-7.
After the captain found himself back him the pavilion it became apparent the end was near for the visitors' innings, with Binura Fernando chipping one up to to Moeen Ali for a score of two off Willey who ended with figures of 3-44, and both Dushmantha Chameera and Praveen Jayawickrama being run out by Billings, leaving Sri Lanka a disappointing 185 all out.
Root leads England to victory after early batting scare
During a difficult T20 series to begin the tour, the one sliver lining for Sri Lanka was that their bowling attack had managed to cause some genuine problems for England's batting line up at times.
They successfully reduced the England to 36-4 in the second match and also enjoyed a four over spell in the final game in which they took 5-19, proving that they could cause a batting collapse.
And it appeared this was happening again when England found themselves 80-4 after 12 overs.
It had seemed as if Morgan's side would breeze to the Sri Lankan total when they reached 54-0 after 4.5 overs thanks to a brutal 43 ball 21 from Jonny Bairstow.
Things quickly began to go wrong for England, though, after Livingstone chipped one up to Chameera at deep mid off, off the bowling of Chamika Karunaratne for nine.
His opening partner Bairstow then went just six balls later when he chopped on to his stumps when trying to cut a back of a length ball from Fernando, leaving England 59-2.
The middle order failed to kick on from the solid platform laid by the openers with captain Morgan being caught behind for six off 17 balls and Billings being caught at gully when trying to drive at a wide one, both off Chameera's bowling.
It could have been even worse for England, however, when Ali was dropped first ball with Perera putting down a relatively simple chance behind the stumps.
Test captain Joe Root remained at the crease though, and quickly began to steady the ship, swiftly moving towards his half century.
The Yorkshire man looked the epitome of calmness throughout his innings, only really giving the tourists a chance when he topped edged a pull shot before being dropped off a difficult chance at fine leg with the score on 116-4.
He was also well supported by Ali at the other end who played an uncharacteristically controlled innings, eventually falling for 28 off 57 balls with his side just 14 runs away from victory.
In the end Root was able to comfortable bring his team home with the winning runs being scored with just 35 overs gone and the 30-year-old finishing up with a not out 79.
England now lead the three match ODI series 1-0 with the next match being played at the Kia Oval Thursday July 1.