Dilshan's second Test century -- which was also the first hundred of the series -- allowed Sri Lanka to declare their first innings on 279 for seven at tea.
Sri Lanka claimed the wickets of Marcus Trescothick (14) and Mark Butcher (6) during the final session to leave England on 89 for two.
Trescothick, fortunate to survive an lbw appeal on eight, was caught at slip off Chaminda Vaas while Butcher was stumped off Muttiah Muralitharan -- a marginal decision by the television umpire.
England captain Michael Vaughan provided some resistance though, finishing the day unbeaten on 50 from 104 balls, his second fifty of the match.
He was supported by former captain Nasser Hussain, who survived a close lbw shout first ball against Muralitharan, to finish on 17 not out.
Dilshan, playing his first test match since March 2001, followed his 63 in the first innings with a sparkling 100 from 121 balls, an aggressive innings that included 13 fours and one six.
The 27-year-old added 153 for the fourth wicket with Mahela Jaywardene (52) to rescue Sri Lanka from a shaky 53 for three after the fall of two early wickets on the fourth morning.
The partnership was a fourth wicket record against England, surpassing the 148 scored by Sidath Wettimuny and Arjuna Ranatunga at Lord's in 1984.
Left-arm spinner Ashley Giles was England's most successful bowler, taking three for 101 from 22 overs to finish with eight for 217 in the game.
England had started the morning brightly as James Kirtley straightened a full-length delivery sufficiently to catch Sanath Jayasuriya's (27) inside edge and flatten his off stump in the third over.
Kumar Sangakkara (10) was surprised by some extra bounce and caught by Paul Collingwood at short leg off glove and pad.
With the lead still a moderate 141, England were back in the game, but Dilshan seized back the initiative with a stunning counter attack.
Scoreboard
Sri Lanka first innings 382 (T.Dilshan 63; A.Giles 5-116)
England first innings 294 (G.Thorpe 57, M.Vaughan 52; M.Muralitharan 4-60, C.Vaas 4-77)
Sri Lanka second innings (overnight 39-1)
M.Atapattu lbw b Giles 8
S.Jayasuriya b Kirtley 27
K.Sangakkara c Collingwood b Giles 10
M.Jayawardene b Flintoff 52
T.Dilshan st Read b Batty 100
H.Tillakaratne c Thorpe b Giles 20
T.Samaraweera not out 23
C.Vaas c Vaughan b Kirtley 20
K.Dharmasena not out 7
Extras (lb-6 nb-5 w-1) 12
Total (for seven wickets, declared) 279
Fall of wickets: 1-33 2-41 3-53 4-206 5-212 6-243 7-272
Did not bat: D.Fernando, M.Muralitharan
Bowling: Kirtley 17-4-62-2 (nb-1), Flintoff 15-3-40-1 (nb-3 w-1), Giles 22-3-101-3 (nb-1), Batty 11-1-47-1, Vaughan 3-0-11-0, Collingwood 3-0-12-0
England second innings
M.Trescothick c Jayawardene b Vaas 14
M.Vaughan not out 50
M.Butcher st Sangakkara b Muralitharan 6
N.Hussain not out 17
Extras (lb-2) 2
Total (for two wickets) 89
Fall of wickets: 1-24 2-50
To bat: G.Thorpe, P.Collingwood, A.Flintoff, C.Read, G.Batty, J.Kirtley, A.Giles
Bowling (to date): Vaas 11-3-25-1, Fernando 6-1-15-0, Dharmasena 8-1-27-0, Muralitharan 10-3-19-1, Jayasuriya 1-0-1-0
