San Antonio attempted 10 shots from the field in the extra period and missed them all while being outscored 5-1.
The Suns went just 2-of-9 from the field in overtime, taking the lead on Marcin Gortat's tip-in with 1:07 remaining. Jermaine O'Neal's jumper with 9.4 seconds remaining gave Phoenix a three-point lead.
San Antonio had a five-point advantage with 50 seconds left in the fourth period, but were outscored 8-3 the rest of the way. Johnson's tying 3-pointer came after Manu Ginobili had missed a free throw for the Spurs that would have clinched a win.
The Spurs lost at home for the third time this season. They have a 22-3 record on their own court, their previous loss having come on Nov. 19 against the Los Angeles Clippers.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need