Koustas gave San Jose State a 14-7 lead with a 28-yard interception return with 10:19 left in the first half, just 17 seconds after the Spartans (1-0) tied it on Scott Rislov's 18-yard TD pass to Kendrick Starling.
The Spartans led 14-7 at the half, then took advantage of two Arkansas State turnovers to score on three straight possessions in the third quarter.
A 5-9 senior, Koustas capped the scoring with a 72-yard fumble return with 13:24 remaining.
Rislov completed just 17-of-34 passes for 174 yards with an interception for San Jose State. Lamar Ferguson paced the Spartans on the ground with 65 yards on 12 carries.
Elliott Jacobs was 12-for-25 for 143 yards with two interceptions for Arkansas State (0-2), which was coming off a 63-7 loss at Virginia Tech.
San Jose State opened a 26-7 lead on Nick Gilliam's 29-yard field goal with 28 seconds to go in the third quarter.
For the Indians (0-2), it was a disappointing performance in the team's first game in the state capital since 1983. Danny Smith paced Arkansas State with 42 yards on 13 rushes.
Arkansas State had five turnovers, which the Spartans turned into 20 points. Indians quarterback Elliot Jacobs was 12-of-25 for 143 yards, with two interceptions. One was returned for a touchdown, and another that led to a field goal.
The Indians took a 7-0 on a 10-yard pass from Jacobs to James Hickenbotham, but the Spartans recovered quickly and needed just eight plays to tie the score. Rislov's 24-yard keeper on the fourth play swung the momentum back in San Jose State's favor.
Rislov capped the drive by hitting receiver Kendrick Starling across the middle for an 18-yard touchdown. Starling broke two tackles on his way to the end zone.
Rislov was playing in his first major-college game after beating out two-year starter Marcus Arroyo during camp. Rislov played one year of junior college at Ellsworth College in Iowa.
After the tying score, San Jose State had the momentum, and two plays later Jacobs handed over the lead. Spartans cornerback Carlos Koustas grabbed a pass from Jacobs at the Indians' 28 and ran untouched into the end zone.
On that play, Jacobs and his receiver, Chuck Walter, miscommunicated with hand signals. Jacobs appeared to call for a quick sideline route. Walter kept running down the sideline, leaving Koustas with an easy pick.
The Indians scored first early in the second quarter, following linebacker Les Echols' second fumble recovery of the game. Six plays later, Jacobs sidestepped a rush and waited for Hickenbotham to slide across the back of the end zone for a wide-open touchdown.
San Jose State's three scores in the third quarter came on a 1-yard run by Oscar Rigg and two field goals by Nick Gilliam, from 22 and 29 yards.
Gerald Jones recovered a fumble and ran it back 72 yards for San Jose State's final score in the fourth period.
Next up for your San Jose State Spartans, the mad as hell University of Washington Huskies.
Washington lost to Michigan on a last second field goal, after the Huskies were given a penalty for having too many players on the field.
That penalty resulted in a 15 yard move towards the goal post for Michigan, which put them in clear view of the game winning field goal.
Look for the Huskies to take out their frustrations on the Spartans, especially if the Spartans defense is not on it's "A" game next saturday at Lake Washington.