The 23-year-old Root, dropped for the final Ashes test during England's 5-0 whitewash Down Under, brought up his 200 with a dab behind square after a well compiled innings that featured 16 boundaries from 298 balls.
"Rooty, to go on and get 100, and then today, the big hundred that we talk about, the game changer, is really important," wicketkeeper Matt Prior, who fell 14 runs short of a century of his own, told a news conference.
"A double hundred at Lord's, what a fantastic effort."
Alastair Cook immediately declared the innings on 575-9 once Root had reached his milestone, leaving Sri Lanka openers Silva and Dimuth Karunaratne to negotiate a tricky spell before tea.
Karunaratne, who successfully overturned an lbw appeal off James Anderson in the first over and offered a chance to the slips soon after, fell to Chris Jordan's third ball in test cricket when on 38, edging to Prior behind the stumps.
However Silva (62) and Sangakkara (32) battled their way through to 140-1 at the close, although the former was lucky to survive a caught behind appeal off Stuart Broad on his way to his fourth half-century, with the third umpire ruling Prior had not claimed the catch cleanly.
"I felt it carry," Prior said. "In your keeping gloves you've got rubber tips and I felt the ball hit the rubber tips. There is no doubt in my mind."
Root, yet to nail a position in the line-up during his short test career, was offered good support by Jordan, Broad and Liam Plunkett as the hosts looked to bat Sri Lanka out of the match against a bowling attack that lacked any real threat after an early three-wicket blast on the first morning of the test.
Root's 200 beat his previous best of 180, also scored at Lord's against Australia last year, and helped rescue his side after they were struggling at 120 for four soon after lunch on the first day.
Having had little luck tossing the ball up late on the opening day, Sri Lanka's bowlers set out to bombard Root and Prior, also returning after injury and being dropped against Australia, with short balls on a pitch that appears set to become easier to bat on as the match progresses.
Prior, who passed 4,000 test runs early in the day, never looked entirely comfortable, eventually falling for 86 when he could only fend a well-directed bouncer from Shaminda Eranga to Silva at forward short-leg, with the pair having put on 171 runs for the sixth-wicket.
Jordan, who along with Sam Robson and Moeen Ali is making his test debut, struck a breezy 19 before becoming Eranga's third victim, while fellow fast bowlers Broad (47) and Plunkett (39) also ticked the total along to help England to their highest score against Sri Lanka, for whom Nuwan Pradeep finished with a career-best haul of four wickets.
"We're not going to blast anyone out on that wicket, we're going to have to build pressure, get control and put a lot of dots on and try get wickets that way," Prior added.
Sri Lanka's Karunaratne was confident his side could avoid the follow-on and then build a score to put pressure back on England, especially with the experienced Sangakkara at the crease and Mahela Jayawardene, who has twice scored centuries at Lord's, to come.
"Kaushal and Kumar batted very well so I think they can go on tomorrow," he said.
"I think 360 is a gettable score and we can avoid the follow on as well."
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- Sri Lanka
- Dimuth Karunaratne