The left-hander scored 112 to lift Sri Lanka to 302-7 after Pakistani paceman Sohail Tanveer notched up career-best figures of 5-48.
Mendis, who took 4-47, then unleashed his quality spin to restrict Pakistan to 238-9 in 50 overs on a slow National Stadium pitch.
For Pakistan, Misbah-ul Haq enjoyed a late flurry, smashing four sixes and three fours during his 70-ball 76 but by then the asking rate of 15 an over was beyond Pakistan's reach.
Skipper Shoaib Malik also hit a subdued 52 off 79 balls with three boundaries but the Pakistani batsmen could not cope with the accurate Sri Lankan bowling.
Sri Lanka, who qualified for the Super League stage with two carry over points, boosted their chances of reaching the July 6 final with the victory.
They now have four points and take on Bangladesh on Monday.
The defeat left Pakistan all but out of the event.
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They now have to win both their matches against India (Wednesday) and Bangladesh (Friday) and hope India also lose to Sr