Lanning's 104 came in 98 balls and included 13 fours as she laid the platform for Australia's 259-6.
England's openers put on 92, but once Heather Knight (38) and Charlotte Edwards (58) were parted the hosts collapsed.
They lost their last seven wickets for 40 runs, being bowled out for 196 - Megan Schutt taking 4-47.
Having lost the first of the seven-match multi-format Ashes series in Taunton on Tuesday, the Southern Stars fought back impressively to claim the two points and draw themselves level.
With the final ODI in Worcester on Sunday, England will look to claim a slender lead before the Test and three Twenty20 internationals.
