Anaheim let a three-goal lead get away but Niedermayer came through to end a four-game Ducks' losing streak. It was the opener of Anaheim's seven-game homestand.
Bobby Ryan scored 6:52 into the second period to give the Ducks a 3-0 lead but Jeff Halpern and Steven Stamkos delivered goals 18 seconds apart later in the period to bring Tampa Bay within one. It was the 14th goal of the season for Stamkos.
Martin St. Louis tied it 1:38 into the third and the teams headed for the fifth overtime played Thursday in the NHL's eight-game schedule.
Tampa Bay's Ryan Malone was called for cross-checking just 11 seconds into the extra period and Niedermayer quickly took advantage by scoring on a slapshot.
Jonas Hiller got the win with 21 saves. Mike Smith made 23 stops for the Lightning.