Tafralis completed 11-of-18 passes for 209 yards and James Jones finished with six catches for 106 yards and two touchdowns for the Spartans (9-4), who won their first bowl game since 1990 when the squad crushed Central Michigan by a final of 48-24 in the California Bowl.
John Broussard added four catches for 106 yards and a touchdown in the victory.
Rodney Ferguson rushed for 102 yards for the Lobos (6-7), who have lost their last five bowl games, with their most recent setback before this contest coming in the 2004 Emerald Bowl against Navy. Ferguson also added eight catches for 78 yards.
New Mexico quarterback Chris Nelson completed 17-of-26 passes for 188 yards and a touchdown in the loss.
After a scoreless opening quarter, San Jose opened the scoring on the first play of the second quarter after Tafralis connected with Broussard on a 76- yard catch-and-run touchdown over the middle to give the Spartans a 7-0 lead.
On the ensuing kickoff, DeAndre Wright ripped off a return of 60 yards to the San Jose State 40-yard line. The Lobos then moved the football down to the three-yard line, but Ferguson fumbled and Damaja Jones recovered for the Spartans.
With just under four minutes left in the first half, San Jose State took a 13-0 lead after Jones hauled in a 36-yard touchdown pass from Tafralis down the left sideline. SJSU missed the extra point following the touchdown. Jones also had a catch for 19 yards on the scoring drive that put the Spartans inside New Mexico territory.
The Lobos got on the board with 1:11 left in the first half after Kenny Byrd drilled a 40-yard field goal to make it 13-3.
With 4:33 left in the third quarter, the Spartans increased their lead to 20-3 after Jones caught his second touchdown of the game, a 24-yard reception in the back left corner of the end zone.
Early in the fourth quarter with his team driving, Ferguson fumbled for the second time in the game and San Jose State recovered the loose ball on its own 29-yard line to end New Mexico's scoring threat.
The Lobos made it 20-5 late in the contest after San Jose State punter Waylon Prather conceded a safety.
After getting the football after the free kick, New Mexico made it 20-12 with just 15 ticks left after Marcus Smith hauled in a 15-yard touchdown pass from Nelson.
The Lobos went for an onsides kick following Smith's score, but touched the football before it went 10 yards.
The Spartans are now 5-3 in bowl games in their school history...San Jose State leads the all-time series with New Mexico at 10-4-1...
The last bowl win for New Mexico was a 28-12 decision against Western Michigan in the 1961 Aviation Bowl, leaving the squad with a 2-7-1 mark in the postseason...The Lobos outgained the Spartans in total yards, 377-280...New Mexico lost four fumbles.