The aggressive Plunkett has been a revelation since his return to the test arena after seven years in the wilderness, and after taking five for 64 in the first innings, the Yorkshire seamer was again England's most dangerous bowler.
He accounted for Dinesh Chandimal (seven) and Dhammika Prasad (zero) in consecutive balls but crucially England could not remove Mathews (79 not out) who will resume after lunch alongside Rangana Herath (seven not out).
After Kumar Sangakkara (55) scored a world record-equalling seventh consecutive test half century, Sri Lanka started the day on 214 for four with Mahela Jayawardene and Mathews well set.
Already trailing by 106 runs and looking to restrict their fourth-innings target, England needed early wickets to restrict the visitors.
By the time the new ball was available after the seventh over of the day, Jayawardene (79) and Mathews had scored freely, adding 40 quick runs to their lead with the captain moving to his 15th test half-century.
Jayawardene survived a dropped chance but eventually departed nicking a wide James Anderson delivery to wicketkeeper Matt Prior, but importantly the senior batsman had added 92 for the fifth wicket with Mathews.
After toiling for much of the morning, England were buoyed when Plunkett had Chandimal caught hooking by Gary Balance at deep square leg before Prasad fended a bouncer to a diving Joe Root at third man on the very next ball.
For the second time in the match, Mathews stoutly kept Plunkett's hat-trick ball at bay before setting about increasing his side's advantage with a string of crushing boundaries.
The first test of the two-match series ended in a draw at Lord's last week.
(Editing by Sudipto Ganguly)
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