San Jose State (0-2) had 305 yards of total offense, but had a punt blocked and turned the ball over two times. Deonce Whitaker had 66 yards on 18 carries.
Brown had scoring runs of 12 and 5 yards and Purify had a 30-yard TD run in the first quarter to give Colorado a 21-0 lead.
After San Jose State's Nick Gilliam hit the left upright from 50 yards out on the game's first possession, Colorado struck quickly, marching 67 yards on 11 plays Brown's 12-yard run.
Strong safety Michael Lewis' diving interception of a pass thrown by Marcus Arroyo at the San Jose 42 let to Brown's 5-yard scoring run off right tackle.
Colorado used a blocked punt by Kori Mossoni to set up Purify's 30-yard touchdown run with 18 seconds left in the quarter.
Gilliam got San Jose State on the board early in the second quarter with a 19-yard field goal. The Spartans stopped Brown on a fourth-and-goal at their own 2, but three plays later Donald Strickland made a juggling interception at the 3 and dove into the end zone.
Ochs connected with Derek McCoy on a 33-yard scoring strike with 12:28 left, giving Colorado a 35-3 lead. Arroyo hit Edell Shepherd on a 5-yard TD pass to get San Jose State to 35-9 at halftime.
The Buffaloes increased their lead to 44-9 in the third quarter. Brown capped an 80-yard opening drive with a 1-yard run and Flores kicked a 19-yard field goal.
Jeff Brunson caught his first touchdown pass, a 62-yarder from backup quarterback Bobby Pesavento 2:35 into the fourth quarter for Colorado. The Spartans got an 11-yard touchdown run from Jarmar Julien with 8:06 left in the fourth quarter.