Several batsmen spent time in the middle, Thilan Samaraweera leading the way with 49, as Sri Lanka chased down a target of 213 with five overs to spare.
As Sri Lanka captain Tilakaratne Dilshan (123) and fellow opener Tharanga Paranavitana (103) both made first innings hundreds, the tourists decided to alter their batting line-up second time around.
Both century-makers had retired and on Monday off-spinner Jamie Dalrymple became the first bowler from county side Middlesex to take a wicket in the match when he had Lahiru Thirimanne and Samaraweera caught at slip.
Sri Lanka lost two wickets on 181 but Farveez Maharoof (17) and Rangana Herath (11) saw the islanders to victory.
Middlesex, 26 for one overnight, were dismissed for 161 with seam bowler Chanaka Welegedara (three for 39) and spinner Ajantha Mendis (three for 28) doing the bulk of the damage.
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Sri Lanka now play the England Lions, the national A side, in a four-day match starting at Derby on Thursday before facing E