Finland, playing under stand-in coach Olli Huttunen who replaced Stuart Baxter last week, were helped by a Mikael Forssell hat-trick having lead just 1-0 at the break courtesy of Mika Vayrynen's 39th minute goal.
Kasper Hamalainen's grabbed a second four minutes after the interval before the floodgates opened. Forssell, who has not scored for Bundesliga side Hanover 96 this season, grabbed his first on 51 minutes before adding two close range strikes on 59 and 78 minutes.
Finland's 39-year-old substitute Jari Litmanen, who is expected to retire after making a record 137 appearances for the national side, was also among the scorers with a 71st minute penalty.
A second for Hamalainen and one for Roni Porokara completed the goal scorers.
Finland are fifth in Group E with three points from four games, while San Marino remain rock bottom with five defeats in as many matches. Netherlands lead the group.
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