The Timberwolves won their third in a row, putting on a fourth-period charge after trailing by seven entering the final quarter.
Minnesota had a four-point advantage with 1:30 left, but Andre Iguodala hit a 3-pointer for the Warriors and then made two free throws with 27 seconds left to put Golden State in front.
Martin, however, hit his jumper off a feed from Kevin Love to bring the Timberwolves back to the .500 mark. Martin was playing despite having suffered a lacerated finger on Tuesday in a game against Utah.
Both Martin and Love scored 26 points with Love adding 14 rebounds and eight assists. Nikola Pekovic also had 14 rebounds to go with his 22 points.
The Warriors, who fell 3 1/2 games behind the Los Angeles Clippers at the top of the Pacific Division, were led by 33 points and 15 assists from Stephen Curry.
2014: The Year in Music [PHOTOS]