The Warriors were clinging to a 100-99 lead with 2:12 remaining when O'Neal sank a 2-pointer to provide the difference.
The Pelicans' Anthony Davis answered with a basket with 47 seconds left, and after O'Neal missed a jumper 23 seconds later, Eric Gordon's final 3-point try for New Orleans wouldn't fall, wrapping up Golden State's win.
O'Neal finished with 18 points with eight rebounds and David Lee supplied 19 and seven for the Warriors, who began a four-game road trip with a victory.
Stephen Curry (16 points, nine assists, eight rebounds) and Harrison Barnes (14 points) also reached double figures.
Ryan Anderson supplied 21 points and 12 rebounds for New Orleans.
Jrue Holiday added 17 points and dished off seven assists.