Halak had an in-close stop on league goals leader Steven Stamkos in the first, and made a glove save on Brett Connolly during a second-period breakaway.
Schwartz, taken 14th overall in the 2010 entry draft and making his NHL debut, put St. Louis up 2-0 from just outside the crease on the power play with 35.5 seconds left in the first.
Patrik Berglund and David Perron also scored for the Blues, who became the first NHL team (46-19-8) to reach 100 points this season.
Brendan Mikkelson got a late third-period goal for Tampa Bay, which is seven points behind eighth-place Washington in the Eastern Conference.
The Blues were without left wing Andy McDonald, who hurt his right shoulder in Thursday's game against Carolina and is week-to-week.
Berglund put the Blues ahead 1-0 on a short-handed goal from the slot off a nice pass by Alex Pietrangelo during a 2-on-1 at the 15-minute mark of the first period.
Tampa Bay has allowed 11 short-handed goals this season. The Lightning, on the other hand, have scored just once while being short-handed.
Perron made it 3-0 when he beat Dwayne Roloson from the right circle 2:47 into the second.
Mikkelson got his first NHL goal, coming in his 116th game, with 4:11 to play.
St. Louis won both games between the teams this season, out-scoring Tampa Bay 6-1.
Notes: Lightning captain Vincent Lecavalier (hand) missed his 13th consecutive game. ... St. Louis C Jason Arnott was rested. ...The Lightning recalled C Trevor Smith from Norfolk of the AHL with C Nate Thompson out because of an upper-body injury. ... Tampa Bay is finalizing a contract with G Sebastien Caron, who has been playing in Germany. The move would allow the team to return rookie G Dustin Tokarski, called up after starting G Mathieu Garon was sidelined by a groin injury on March 6, to Norfolk.