Sri Lanka bundled out Kenya for just 127 runs in 37.5 overs to win the match by a big margin of 129 runs in the Sharjah Cup on Sunday.
Off-spinner Muralitharan picked up 3 wickets in the 37th over to finish the match, skipper Sanath Jayasuriya also bowled well picking up 2 wickets for 21 runs in his 8 overs.
Earlier, Jayasuriya passed 9,000 runs in one-day internationals while in-form Kumar Sangakkara thumped his second successive century to help Sri Lanka reach 256 for five wickets against Kenya in their alloted 50 overs.
Jayasuriya, playing in his 299th match, needed seven runs to become the fourth highest run-scorer in the world, a task he achieved comfortably during his innings of 36 off 45 balls.
India's Sachin Tendulkar (12,219) and Mohammed Azharuddin (9,378) and Sri Lankan Aravinda de Silva (9,284) are the only other players to have scored more than 9,000 runs.
Left-hander Sangakkara, who scored 100 not out against Pakistan on Friday, produced another scintillating unbeaten knock of 103, made off 108 balls, to put Sri Lanka in a commanding position in their bid to avenge their 53-run World Cup loss against Kenya in February.
Jayasuriya and Avishka Gunawardene, who opened the innings in place of Marvan Atapattu, gave Sri Lanka a solid start by contributing 53 before the two fell in the space of 14 balls.
Jayasuriya fell leg before to a Tony Suji delivery that pitched outside the leg stump, as repeated TV plays showed, but umpire Avi Jayaprakash had no hesitation in raising his finger. Gunawardene (24) then nicked to wicketkeeper Kennedy Obuya.
Kenya threatened to wrest the initiative when Collins Obuya got rid of Atapattu for 19, but Sangakkara dug in with Hashan Tillekaratne (43) to share a 93-run stand.
Sangakkara, who exchanged heated words with Kennedy Obuya when his appeal for caught behind was turned down by umpire Jayaprakash, completed his century from the last ball of the innings.
