Junior midfielder Filip Pavisic pounced on a rebound in the 86th minute, and buried a shot past Tulsa goalkeeper Jake McGuire, for the first goal of his Billiken career.
SLU, which outshot Tulsa 14-9 in the game and controlled the action for much of the night, threatened to score multiple times late in the match.
But it wasn't until a corner kick by junior David Graydon, which led to a header attempt by senior Anthony Manning, that Pavisic found himself alone in front of the net with the ball and plenty of space to shoot at.
The former Serbian junior national player didn't hesitate, as he blasted a shot into the right side of the Tulsa goal for the only score of the night.
Freshman goalkeeper Sascha Otte earned the win in his first collegiate start for the Billikens (1-0).
SLU will be back in action at Hermann Stadium on Sunday, when it will host Virginia Tech (1-0), which also won its first match of the season, Friday night against SIU-Edwardsville.
The opening kickoff for Sunday's contest between the Billikens and Hokies is scheduled for 7 p.m.
Scoring by Period ... 1 ... 2 ... Final
Tulsa ........................... 0 ... 0 ... 0
Saint Louis ................. 0 ... 1 ... 1
SLU - 85:21 - Filip Pavisic (1), assisted by David Graydon, Anthony Manning.