Anderson, who had never rushed for 100 yards in a game before gaining 157 in a victory last weekend over Louisiana-Monroe, carried the ball 36 times in setting a new career high for the second time in less than a week.
Moore completed 19-of-24 passes for 254 yards. He was intercepted once. Two of his touchdowns went to Jeremy Williams on passes of 51 and 21 yards. His other TD pass went for 23 yards to Alan Mitchell on what was Mitchell's first college catch. Williams finished with six catches for 124 yards.
June Jones' spread offense continues to be a work in progress at SMU, but showed promise in spurts.
Bo Levi Mitchell was 21-of-44 for 256 yards and three TDs. He was intercepted twice by David Skehan and Josh Lumar, however, and the Mustangs were doomed by a poor first half in which they fell behind 31-7.
Tulane gave SMU hope with a pair of turnovers in the third quarter.
Kasey Stelly's fumble, recovered by Derrius Bell on the Tulane 33, set up Thomas Morstead's 25-yard field goal.
The Green Wave then drove to the SMU 18, only to turn the ball over again when Moore's first-down pass was intercepted by Justin Smart and returned 35 yards to the SMU 45. That led to Morstead's 49-yard field goal.
Facing fourth-and-3 on the Tulane 31 on its next series, SMU converted when Mitchell found Emmanuel Sanders for a 13-yard gain. Mitchell went right back to Sanders on the next play for an 18-yard score that pulled the Mustangs to 31-20 early in the fourth quarter.
Tulane managed only Ross Thevenot's 33-yard field goal in the second half, which gave the Green Wave a 34-20 lead with about four minutes to go.
Mitchell's 13-yard touchdown pass to Terrance Wilkerson pulled SMU to 34-27 with 2:03 left.
SMU then chose to kick deep, but couldn't stop Anderson, whose 40-yard run to the SMU 42 on the second play of Tulane's final drive sealed the victory.