Mathews (149 not out) scored his fourth test century, and second of the series, as he put on 149 with Rangana Herath (48) for the eighth wicket.
England’s only joy came with the last ball of the session when Herath was run out by Joe Root as Sri Lanka reached 426 for eight at the break.
The afternoon session resumed with Sri Lanka 311 for seven with captain Mathews unbeaten on 79 alongside tail-ender Herath.
England had taken three wickets for nine runs before lunch but with Mathews cleverly rotating the strike to protect his partner, the pair set about building a healthy partnership.
After being put down by Plunkett on 87 Mathews reached three figures with a cut to the offside.
Herath averages less that 13 with the bat but has a test-best 80 not out and he easily dealt with England’s bowling before going on the attack with a series of pulled and driven boundaries.
Mathews and Herath continued to score at will as the game, which appeared to be England’s for the taking after two days, continued to run away from them.
With Mathews one run short of his 150 Herath set off for a quick single but was dismissed by a quick throw from Root.
After Kumar Sangakkara (55) scored a world record-equalling seventh consecutive test half century on Sunday, 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 and Mathews had scored freely, adding 40 quick runs to their lead.
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 took two wickets in two balls for the second time in the match.
After James Anderson had removed Jayawardene (79), Plunkett accounted for Dinesh Chandimal (seven) and Dhammika Prasad (zero) in consecutive balls before Mathews denied him a hat-trick for the second time in the match.
The first test of the two-match series ended in a draw at Lord's last week.
(Editing by Josh Reich)
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