Freese, who went 3-for-4 with a homer and two RBI, doubled home a run and later scored on Matt Adams' two-run blast in the first inning, giving St. Louis a quick 4-0 lead.
His solo shot in the seventh put the Cards ahead 10-2.
Tony Cruz also delivered a bases-empty homer and added an RBI single during a five-run sixth inning that broke the game open as the Cardinals claimed the rubber match of a three-game series between the National League Central rivals.
Jon Jay added three hits, including a two-run double to cap the scoring for second-place St. Louis, which came into the contest trailing NL Central-leading Pittsburgh by 1 1/2 games.
Lynn (13-5) struck out a season-high 11 batters over eight solid innings, surrendering two runs on four hits.
Reds starter Mike Leake (10-5) was roughed up for seven runs on eight hits over five full innings.
Zack Cozart went 2-for-3 with a two-run homer for Cincinnati.