The way he played elicited full-throated roars, and will inevitably bring calls for Harris to get the start when LSU returns to Southeastern Conference play at No. 5 Auburn next week.
''This is obviously how you want to play,'' Harris said. ''That is what I wanted to come out and do tonight. I feel like we did it as an offensive unit and as a team.''
Harris was 11 of 14 for 178 yards and three touchdowns - a statistical line that stood in stark contrast to that of Jennings, whose seven series under center comprised arguably his worst night as a Tiger. Jennings completed two of five passes for 11 yards and no TDs while turning the ball over three times on two interceptions and a fumble.
Coach Les Miles had high praise for Harris, while adding that Jennings will ''have to get better,'' but stressed that he expected LSU to need both quarterbacks and declined to answer a question about who he thought should start at Auburn next weekend.
''We're not going to operate that way,'' Miles said. ''We've kind of always done things in a measured fashion and we'll go back and look at the film and communicate with our team.''
Harris said it was hard for him to take much pleasure in beeing cheered when he entered the game after hearing the same crowd boo several miscues by Jennings.
''It shouldn't be the way it was tonight where we may have somebody booing him,'' Harris said. ''We need to all support him when he is in there. It hurt me to hear anything. I know you shouldn't listen to all of that, but coming from me, I just don't think it was the appropriate way to handle that situation.''
New Mexico State (2-3) trailed 28-0 before its only scoring play on backup quarterback Andrew Allen's 79-yard touchdown run. Aggies starting quarterback Tyler Rodgers was 14 of 31 for 86 yards with two interceptions.
''Tyler was under duress all night,'' New Mexico State coach Doug Martin said. ''That was a hard game for any quarterback to play. At the same time, Tyler's got to take better care of the ball.''
Despite four first-quarter turnovers, LSU (4-1) had an early 14-0 lead, thanks in part to a defensive score by sophomore linebacker Kendell Beckwith on a 27-yard interception return of Rodgers' deflected pass.
Entering the game in the second quarter, Harris let LSU's power running game do much of the work. Still, eight of his first nine passes were completions, and three went for touchdowns.
The righty's most impressive throw came as he scrambled left, hitting fellow freshman Malachi Dupre with a 27-yard scoring strike.
''Brandon came out and showed his ability tonight,'' Dupre said. ''He and Anthony both possess unique skill sets. It was Brandon's night.''
Freshman running back Leonard Fournette rushed for 122 yards and two TDs rushing, including a 17-yard run in which he shed tacklers near the line of scrimmage before racing free to his right.
The calls for Harris built to a crescendo following LSU's first loss of the season to Mississippi State the previous week.
Harris entered that game without about five minutes left and led a pair of quick touchdown drives, and then got LSU in range for a Hail Mary heave, which, if successful, would have completed a miraculous comeback in a game the Tigers trailed 34-10 early in the fourth quarter.
Since Harris entered the game against the Bulldogs, he is 17 of 23 for 318 yards and five touchdowns against only one interception, which came on his Hail Mary attempt.
His touchdown runs came from 1 and 2 yards out, but the second run seemed to be the result of improvisation after he bobbled a high shotgun snap. To get to the end zone, he bowled his way through a heavy hit.
LSU finished with 363 yards rushing, including Terrence Magee's first TD of the season on an 11-yard run. The Tigers' 63 points tied the highest output by LSU since Miles took over as coach in 2005.