He was man-of-the-match, but he blew two superb chances.
France Under-21 international Saint-Maximin was a nuisance throughout for West Ham but was unable to cap his display with a goal, despite having a game-high three shots on target.
Saint-Maxim joined from French club Nice for a reported £16.5m last summer.
"He should have scored but you can see he is a handful and will get people off his backsides," Magpies boss Steve Bruce said.
"He's that little bit of different. He is exciting and quick and if he can learn to be more clinical we will have a player on our hands."