Muralitharan took all five wickets to fall after tea as Australia wilted to 188 for 5 at the close of play in reply to Sri Lanka's first innings total of 296 all out.
Muralitharan dismissed Slater for 96 while Blewett was out for 62. Yet Slater and Blewett had been well in control against the five Sri Lankan bowlers used by the skipper, Sanath Jayasuriya, in the first hour of play.
Slater reached his 50 in 100 balls, hitting four boundaries and a six. Blewett was the slower of the two, reaching his half century in 159 balls with four boundaries.
Slater was lucky when the Sri Lanka wicketkeeper, Romesh Kaluwitharana, first dropped a catch and then missed what looked an easy stumping chance when on 64. The second miss robbed the debutant Rangana Herath of his first Test wicket.
But Muralitharan slowed Australia, dismissing Blewett first and then having Justin Langer out to a doubtful catch by the former Sri Lankan captain, Arjuna Ranatunga. Television replays showed that the ball touched the ground.
Mark Waugh and Ian Healy fell cheaply in the final overs for only nine more runs.
Earlier, Glen McGrath and Damien Fleming ended the Sri Lankan first innings after the hosts added 42 runs to their overnight score of 254 for 6. McGrath claimed the wickets of Kaluwitharana and Nuwan Zoysa and Fleming accounted for Chaminda Vaas.
The highlight of the morning's play was the 41 by Sri Lankan fast bowler Vaas, scored off 58 balls.
(Galle, second day)
Sri Lanka won toss
SRI LANKA - First Innings
(Overnight: 254 for 6)
R S Kaluwitharana b McGrath 25
W P U J C Vaas c Ponting b Fleming 41
R Herath run out 3
D N T Zoysa c Waugh b McGrath 1
M Muralitharan not out 7
Extras (4b 8lb 8nb) 20
Total (106.5 overs) 296
Fall (cont): 7-262 8-288 9-288.
Bowling: McGrath 26.5-7-81-3 (nb7); Fleming 23-6-74-2 (nb1); Miller 23- 1-72-1; Warne 25-11-29-3; Ponting 4-1-7-0; M Waugh 2-1-9-0; Blewett 3- 0-12-0.
AUSTRALIA - First Innings
M J Slater st Kaluwitharana
b Muralitharan 96
G S Blewett b Muralitharan 62
J L Langer c Ranatunga
b Muralitharan 7
M E Waugh c Ranatunga
b Muralitharan 10
*S R Waugh not out 2
I A Healy c Jayawardene
b Muralitharan 4
R T Ponting not out 0
Extras (1b 4lb 2nb) 7
Total (for 5, 83 overs) 188
Fall: 1-138 2-160 3-179 4-182 5-188
To bat: S K Warne, D W Fleming, C R Miller, G D McGrath.
Bowling (to date): Vaas 9-3-31-0; Zoysa 6-1-9-0; Herath 28-5-78-0 (nb1); Muralitharan 31-10-50-5 (nb1); Jayasuriya 9-1-15-0.
Umpires: B C Cooray and D B Cowie.Reuse content