The Wildcats were never able to put the Aztecs away and had only a four-point lead with 1:20 to play. Aaron Gordon then converted an alley-oop pass from T.J. McConnell and McConnell made 1-of-2 from the line to give Arizona a seven-point cushion going into the final 40 seconds.
Arizona has won all of its three games while San Diego State slipped to 1-1.
Gordon added 16 points and nine rebounds for the Wildcats, who held the Aztecs to 34 percent shooting.
Xavier Thames and J.J. O'Brien both scored 19 for the Aztecs.