Sri Lanka, following on, were 403 for six at lunch on the fourth day -- a lead of six runs.
Chandimal, dropped on 69, was 108 not out.
This was his sixth hundred in 27 Tests but first outside Asia.
Chandimal received excellent support from Rangana Herath (37 not out) in an unbroken seventh-wicket stand of 89 that ensured England would have to bat again in a bid to go an unassailable 2-0 up in this three-match series.
Sri Lanka resumed on 309 for five, 88 runs adrift of England's 498 for nine declared built around Moeen Ali's Test-best 155 not out.
At that stage, a second successive innings defeat, following Sri Lanka's innings and 88-run loss in the first Test at Headingley, was still a possibility.
Chandimal was 54 not out overnight and Milinda Siriwardana 35 not out after Sri Lanka captain Angelo Mathews (80) and Kaushal Silva (60) initially kept England at bay.
Play began Monday under a heavily grey sky.
The cloud cover promised ideal conditions for England pacemen James Anderson and Stuart Broad, who were just five overs into a spell with the new ball.
Siriwardana had not added a run to his overnight score when he edged Anderson straight to Alex Hales at gully to end a stand worth 92.
Chandimal, however cover-drove Broad for four and late-cut Anderson behind point for another boundary.
But he was lucky on 69 when he got an inside edge off Anderson only for diving wicket-keeper Jonny Bairstow to spill the catch despite getting both gloves to the ball.
The gutsy Herath, primarily a left-arm spinner, then saw Sri Lanka to 350 when he pulled Chris Woakes behind square for four.
Chandimal then went into the 90s when he hooked Finn to the fine leg boundary.
An edged boundary off Woakes to third man saw the 26-year-old Chandimal to a 172-ball hundred including 11 fours.
Chandimal ended an excellent session for Sri Lanka in style by cover-driving Woakes for four off the last ball before lunch.