Muralitharan broke the record in the morning as he claimed 6 for 55 in 35 overs and England were bowled out for 281, securing a valuable 93 first-innings lead in a low-scoring game.
Veteran opener Sanath Jayasuriya, who later announced the match would be his final Test, was out for 78 as the hosts reached 167 for two at stumps to lead by 74 with two days remaining.
Tied with Warne overnight, Muralitharan was forced to wait until his second spell of the morning before moving off the 708-wicket mark, bowling Paul Collingwood with a delivery from around the wicket that nipped straight on.
England had resumed on 186 for six, trailing Sri Lanka's first innings total by two runs, but repelled Muralitharan and the host's bowlers during the first hour as Collingwood (45) and Ryan Sidebottom (31) added 57 runs for the seventh wicket.
Lasith Malinga picked up the wicket of Sidebottom before Murali brought the house down. The landmark wicket of Collingwood was greeted with loud firecrackers all around Asgiriya International Stadium and wild celebrations from a full house that included hundreds of children from his old school, his family and closest friends.
"The England batsmen played well in the morning and it was getting a bit tougher for me as this pitch is getting slower and slower," Muralitharan told reporters.
"The delivery to Collingwood was supposed to be an off break but it went straight on so I guess was lucky."
The 35-year-old added to his tally in the next over with the wicket of Matthew Hoggard (15), who was brilliantly stumped down the leg-side by wicketkeeper Prasanna Jayawardene.
Muralitharan finished the innings with figures of 6-55, the 61st time he has taken five wickets in an innings.
Later, Sri Lanka prospered through Jayasuriya’s quickfire knock, that included six fours in one James Anderson over.
SCORE BOARD
SRI LANKA (I Innings): 188
ENGLAND I Innings (o/n: 186/6)
Cook lbw Vaas 0
Vaughan c Silva b Muralitharan 37
Bell c Silva b Muralitharan 83
Pietersen lbw Muralitharan 31
Collingwood b Muralitharan 45
Bopara c P J’wardene b M’tharan 8
Prior c Mubarak b Fernando 0
S’bottom c P J’dene b Malinga 31
Hoggard st P J’dene b M’tharan 15
Anderson lbw Vaas 9
Panesar (not out) 2
Extras (B-6, LB-1, NB-11, W-2) 20
Total (all out, 93.1 overs) 281
Fall of wickets: 1-0, 2-107, 3-132, 4-170, 5-182, 6-185, 7-242, 8-266, 9-272.
Bowling: Vaas 18.1-3-76-2, Malinga 20-2-86-1, Muralitharan 35-14-55-6, Jayasuriya 2-0-9-0, Fernando 18-2-48-1.
SRI LANKA (II Innings)
Vandort c Bell b Anderson 49
Jayasuriya lbw b Hoggard 78
Sangakkara (batting) 30
Jayawardene (batting) 0
Extras (B-5, LB-5) 10
Total (for 2 wkts, 52 overs) 167
Fall of wickets: 1-113, 2-166.
Bowling: Hoggard 11-3-28-1, Sidebottom 11-2-22-0, Panesar 18-1-53-0, Anderson 9-2-50-1, Bopara 3-1-4-0.