Skipper Jayawardene made a fluent 65 and Pakistan's Yousuf a solid 66 after Asia had elected to bat on a good track in the day-night game.
Yousuf also became the third Pakistani batsman to complete 8,000 runs in one-day internationals during his 74-ball knock after retired Inzamam-ul-Haq and Saeed Anwar.
Debutant seamer Morne Morkel of South Africa was the most successful bowler with 3-68. His brother Albie and Zimbabwean seamer Elton Chigumbura grabbed two wickets apiece.
Indians Virender Sehwag and Sourav Ganguly had put the Asian side on course for a big total with a brisk 68-run stand for the second wicket off just 49 deliveries.
Opener Sehwag smashed a 42-ball 45 with one six and seven fours before inside-edging a Chigumbura delivery on to his stumps.
Left-handed Ganguly fell in similar fashion, but to Morne Morkel. The former Indian captain hit seven fours in his 29-ball 32.
Jayawardene, who led Sri Lanka to the World Cup final in April, and Yousuf then built on the Indian duo's efforts as they put on 94 for the fourth wicket to ensure the African side chased a stiff target under lights.
The Sri Lankan hit one six and seven fours in his 62-ball knock before being caught by Shaun Pollock off Kenyan off-spinner Steve Tikolo while attempting a big shot.
Indians Yuvraj Singh (31) and Harbhajan Singh (20) scored valuable runs in the closing overs to help their team cross the 300-mark.