The Warriors built a 17-point lead during the second quarter, but the Suns rallied and the teams staged a close battle throughout the final period.
The jump shot by Landry put the Warriors in front 87-84 and Golden State regained the ball with a chance to clinch the contest. Brandon Rush missed a 3-pointer for the Warriors, however, giving Phoenix an opportunity to tie it.
Golden State spoiled those hopes by twice fouling to prevent the Suns from getting off a 3-point try and Phoenix wound up getting just one point from Goran Dragic at the foul line during the final 6 seconds.
Landry scored 17 points off the bench to lead the Warriors and Klay Thompson had 16 points to go with eight rebounds.
Stephen Curry, who signed a 4-year contract extension with the Warriors earlier in the day, had five points and seven rebounds.
Phoenix opened a season without Steve Nash at point guard for the first time since 2003. Dragic started at that position for the Suns in their season opener and he came through with 17 points, six rebounds and eight assists.