Pin didn't help herself by double-faulting twice while serving at 1-5 to set up double match point. Williams finished it by pouncing on a slow first serve and whacking a powerful crosscourt forehand winner.
Williams next faces 17th-seeded Daniel Hantuchova of Slovakia, who beat Asian wild-card entry Akgul Amanmuradova 6-4, 6-1. Williams won the Australian Open in 2003 and 2005, and missed the 2004 event because of injuries.
Eighth-seed and French Open champion Justine Henin-Hardenne moved on with a 7-6 (2), 6-1 win over Hana Sromova, who badly turned her right ankle at 1-1 in the second set and lost the next five games.
Trailing 3-1 in the first set tiebreaker, Davenport rallied after Sprem double-faulted, winning six of the last seven points and claiming the first set with consecutive forehand winners.
Davenport will now face 25th-seeded Maria Kirilenko, who had a 7-6 (1), 6-4 win over fellow Russian Galina Voskoboeva.
No. 7 Ivan Ljubicic, No. 8 Gaston Gaudio, No. 11 David Ferrer, No. 16 Tommy Robredo and No. 18 Mario Ancic advanced.
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