Day-Lewis, 55, previously won for his work in "My Left Foot" and "There Will Be Blood."
No other man had ever won the Best Actor Oscar three times.
"I really don't know how any of this happened. I have received so much more than my fair share of good fortune," Day-Lewis said upon collecting his latest prize.
"Lincoln" went into Sunday's competition with a leading 12 nominations, including one for Best Picture. The Steven Spielberg-directed film picked up only one other award -- Best Production Design -- at the ceremony.
Celebrity Families of 2014 [PHOTOS]