Russell finished 20-of-23 for 197 yards for the Tigers, who were eager to make up for an overtime home loss to No. 10 Tennessee five days earlier in which they blew a three-touchdown lead.
LSU started this one with a brief defensive hiccup before rediscovering its rhythm, holding Mississippi State to 56 yards rushing and beating the Bulldogs for the sixth straight time.
LSU (2-1, 1-1 Southeastern Conference) scored on three consecutive first-half possessions and rolled to their 13th victory over Mississippi State in 14 meetings. LSU has outscored the Bulldogs 202-26 during the past five games.
Russell hit Bowe with scoring passes covering 14 and 44 yards, the latter coming after Bowe bounced off Bulldogs freshman De'Mon Glanton at the 20 and coasted into the end zone.
Mississippi State (2-3, 0-3) has been outscored 60-17 in back-to-back home losses to Georgia and LSU, both top-10 teams. It doesn't get any easier next week - the Bulldogs play Florida at The Swamp.
Mississippi State came out firing against an LSU pass defense that entered as the worst in the SEC. On the fifth play from scrimmage, Omarr Conner hit a wide-open Joey Sanders from 66 yards out for a short-lived 7-0 lead.
After that, it was all LSU. The Tigers forced three consecutive three-and-outs, scored three straight times and were never again threatened.
LSU scored 17 quick points, using a bit of trickery to take the lead. Xavier Carter took an end-around handoff 36 yards into the end zone late in the first quarter to make it 10-7.
On the Tigers' next possession, Russell and Bowe hooked up for a 14-yard score to extend the lead to 10.
Colt David started the scoring for LSU with a 30-yard field goal in the first quarter to make it 7-3.
Joseph Addai rushed 17 times for 86 yards for LSU. He and fullback Jacob Hester each had a 1-yard touchdown run for the Tigers.
Conner was 9-of-22 passing for 141 yards for the Bulldogs.
Jerious Norwood, Mississippi State's leading rusher and a preseason all-SEC selection, left the game late in the second quarter with a mild concussion after he was hit hard by LSU's Kenneth Hollis and Jessie Daniels.
Norwood, who entered averaging 76 yards, rushed for nine yards on seven carries and had two receptions for 32 yards before he was injured and didn't return.
Backup Brandon Thornton led the Bulldogs with 46 yards rushing on four carries.