Franzen scored three times in a 3:26 span of the first period and had a fourth goal in the third to go along with two assists.
Steve Yzerman and Norm Ullman shared the previous record with five points. Franzen matched Carl Liscombe's mark of four goals, set in 1945, and matched by Ted Lindsay matched in 1955.
Anaheim's Joffrey Lupul was the last player to score four goals in a playoff game in 2006 against Colorado.
Franzen was originally credited with scoring a playoff record-tying four goals in a period, but had the first one taken away by a scoring change. Todd Bertuzzi earned the one Franzen lost.
Detroit, facing elimination, led 5-0 after the opening frame and 7-1 following Franzen's fourth goal at 7:33 of the third period.
Pittsburgh's Mario Lemieux scored four goals in a postseason period en route to tying an NHL-playoff record five on April 25, 1989, against Philadelphia. Tim Kerr of the Flyers netted four in a period on April 13, 1985, against the New York Rangers — three being scored in a record of 3:24.