Lockhart finished with 16 points and Ian Carter had 16 points and 11 rebounds as the Panthers won their fifth straight game and improved to 13-4 overall and 7-2 in the GLVC.
UMSL dropped to 11-6 overall and 4-5 in the league.
In a game that featured 16 lead changes and 13 ties, the Panthers made the biggest plays down the stretch to end some frustration against the Tritons, who defeated them three times last season.
The game was deadlocked once and for all at 70 after Joshua McCoy's free throw with 58 seconds left. The Panthers worked the ball around and into the hands of Lockhart, who coolly drained the 3-pointer from the left wing to put the Panthers up 73-70.
UMSL's Darian Cartham missed a 3-point attempt at the other end, Ian Carter grabbed his 11th rebound of the game and got the ball back into the hands of Lockhart, who dribbled through traffic and was fouled with 11.5 seconds left.
Lockhart, a Chaminade High School product in St. Louis, drained the ever-important first free throw to put the Panthers up four (74-70) with 11 seconds left, missed the second, but the Tritons couldn't not answer as DU - picked for second in the GLVC West preseason poll of league coaches - upended preseason favorite UMSL.
"I'm proud of the guys for the grit they showed on the road," Drury coach Steve Hesser said. "That's a very good UMSL team, and we did a solid job of sharing the basketball late and coming up with the big plays when we needed them."
Alex Hall added 13 points and hit three 3-pointers (pushing his career total to 318, just 33 behind all-time leader Matt Miller).
Lockhart had an uncharacteristic eight turnovers, but also had six assists and two steals in his 38 minutes of court time.
Carter made 8 of 11 shots as Drury hit 55 percent (27 of 49) for the game, including a 7-for-12 effort from 3-point range (58 percent). UMSL shot just 42 percent from the field (22 of 52), but went 18 of 19 at the free-throw line (95 percent).
Cameron Adams added 10 rebounds as the Panthers beat the Tritons 28-25 on the boards.
Drury concludes its three-game road swing at William Jewell on Thursday before returning home next Saturday to host Rockhurst in the annual "Overflow The O'" game.