England, who won by 43 runs in Brisbane on Tuesday, scored 258 for nine against Sri Lanka on Friday before bowling them out for 163 in 43.4 overs to win by 95 runs on the fast and bouncy wicket at the WACA Ground in Perth.
Man of the match Collingwood scored 100 from 127 balls with four boundaries and two sixes, reaching his first one-day international century in the 50th over.
The Durham right-hander was caught at point on the final ball of the innings as Sri Lanka pace man Dilhara Fernando claimed career-best figures of four for 48.
Collingwood, who came to the crease at 39 for three in the ninth over, added 110 with White.
The pair beat the previous seventh-wicket record for England set by former captain Mike Gatting and Paul Downton of 86 against India in Poona in 1984-85.
Sri Lanka's batsmen were unable to settle into a rhythm in reply, losing four wickets for 46 in the first 11.3 overs as veteran pace man Andy Caddick captured three for 30 from his 10
Mahela Jayawardene (30) and Russel Arnold added 45 for the fifth wicket before Arnold combined with Thilan Samaraweera (27) for a sixth-wicket stand of 53.
Arnold top-scored with 44 before he was caught behind off the bowling of Steve Harmison in the 42nd over at 162 for eight.
Left-arm opening bowler Chaminda Vaas had given Sri Lanka the initial advantage, taking three for 36 from his 10 overs including the wickets of openers Marcus Trescothick for 11 and Nick Knight for 15.
England began the triangular series with two consecutive losses against Australia last week but now lead the standings after two wins against Sri Lanka.
Australia play Sri Lanka in Perth on Sunday.
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