Corbin took over the Jazz after Jerry Sloan surprisingly resigned Thursday in the midst of his 23rd season with the club.
It appeared Corbin might win in his debut when Utah jumped to a 12-point lead after one period, but the Suns limited the Jazz to 27 points during the second half to capture their third straight.
The score was tied with 7 minutes to go before Phoenix finished the contest on a 20-8 run.
Nash scored 18 points and Hakim Warrick added 16 off the bench. Robin Lopez contributed 14 for the Suns.
Both C.J. Miles and Deron Williams had 19 points for Utah