Point and Nikita Kucherov each had a goal and an assist, and Andrei Vasilevskiy won his 100th NHL game with 35 saves for the Lightning (31-7-2), who finished a month without a regulation loss for the second time in Tampa Bay history (13-0-1), joining the 2003-04 team that went 6-0-1 in October.
The Lightning are 14-0-1 since losing 3-1 to the Ducks on Nov. 27.
WATCH: [All Lightning vs. Ducks highlights]
"Got to give the boys credit in there, they had a pretty productive December," Tampa Bay coach Jon Cooper said. "Especially the amount of goals we've given up here in the last little bit, to play the way we did tonight and only give up one against a really good hockey team, it was pretty satisfying."
Nick Ritchie scored, and John Gibson made 33 saves for Anaheim (19-15-7), which has lost six games in a row, the past two in the first minute of overtime.
"I thought the effort level was there," Ducks captain Ryan Getzlaf said. "We had a few mental errors, obviously, throughout the game, and those things happen. Our goaltender made some good saves, so we showed strides tonight, but we have to get better."
Kucherov, who extended his point streak to 11 games with his sixth straight multipoint game, slid a pass from the neutral zone to Point at the Anaheim blue line. Point held off Ducks defenseman Brandon Montour as he skated through the slot, and then lifted a backhand over Gibson's right pad for his Lightning-high 23rd goal.
Kucherov gave Tampa Bay a 1-0 lead with his 19th goal at 6:06 of the first period.