New Zealand went to lunch at 174 for seven with their target of 504 all but insurmountable after Muralitharan orchestrated yet another batting collapse.
He has the impressive figures of four for 45 from 22 overs as the New Zealand batsmen failed to cope with his mesmerising spin.
After resuming the day at 75 for two, and still with an outside chance of reaching their target, Stephen Fleming and Mathew Sinclair staged a hopeful third-wicket partnership.
But when they had put on 55 runs, taking New Zealand's score to 115, Lasith Malinga made the breakthrough Sri Lanka were seeking.
With his first ball to Fleming he found the edge of the bat for Kumar Sangakkara to take a standard catch behind the stumps and the New Zealand captain was out for 27.
Muralitharan struck for the first time of the morning, taking Sinclair for 37 and followed up by trapping Nathan Astle in front for nine and bowling Brendon McCullum for 17 to add to the dismissal of Craig Cumming at the start of the innings on Sunday.
Chaminda Vaas completed the morning rout with the dismissal of Jacob Oram. The New Zealand all-rounder, struggling with a hamstring injury, was unable to deal with a Vaas flyer and was out leg before wicket.
Daniel Vettori was not out 10 with James Franklin yet to score at lunch.
Scoreboard at lunch:
Sri Lanka 1st innings 268 (K. Sangakkara 156 n.o., C. Silva 61; C. Martin 3-50, D. Vettori 3-53)
New Zealand 1st innings 130 (B. McCullum 43; L. Malinga 5-68, M. Muralitharan 4-31)
Sri Lanka 2nd innings 365 (C. Silva 152 n.o., C. Vaas 47; Vettori 7-130)
New Zealand 2nd innings
Fall of wickets: 1-56, 2-60, 3-115, 4-139, 5-156, 6-161, 7-163
Toss: Sri Lanka
Umpires: Simon Taufel (AUS), Brian Jerling (RSA)
Match referee: Javagal Srinath (IND)
Series: New Zealand 1-0