It was Howard's fifth career game of 40 or more points. The effort also broke the tourney record of 38, set by Marquette's Matt Carlino against Georgia Tech in 2014.
"Offensively we're still figuring out who we are, and while we're doing that we need Markus to be Markus," Marquette coach Steve Wojciechowski said.
With Marquette (4-1) clinging to a 60-59 lead with 2 ½ minutes to play, Howard made a layup and hit a free throw to complete a three-point play before adding a 3-pointer to key a game-ending surge.
"My team and coaches gave me the 'go' and I felt very comfortable trying to do what I could," Howard said.
Kellan Grady had 28 points for Davidson (2-4). He scored 14 in the first half to help the Wildcats go up 26-25 at the break.
"There's no doubt this was an absolutely sensational effort by our guys," Davidson coach Bob McKillop said. "This is the kind of effort they're capable of every time they step on the court."
Howard scored 15 first-half points, including a 3-pointer at the buzzer.
Davidson went 0 for 15 from behind the arc, ending a streak making at least one 3-pointer at 809 consecutive games. The previous time the Wildcats didn't make a 3 was Jan. 15, 1994 in a 65-63 win at East Tennessee State.
"That was definitely our biggest point of emphasis on the game, guarding the 3-point line," Howard said.
Marquette, which also got 12 points from Sacar Anim, converted 6 of 17 from behind the arc.
Davidson stayed close by dominating in the paint, outscoring Marquette 34-14.
Marquette: Held its previous four opponents to 36% shooting. Davidson, however, connected for 45.8% (11 of 24) in the first half. The Wildcats ended up at 45.3% (24 of 53).
Davidson: Played the second games in a stretch of nine of 10 road games. It should be a test for how the Wildcats handle adversity heading into the conference schedule in January.
Marquette faces USC in a Friday semifinal.
Davidson will meet Fairfield in the consolation round.