Tejada's second field goal in three attempts gave Arkansas just its third win in 15 bowl appearances.
The win came after ECU's Ben Hartman missed two field goals in the final 1:03 of regulation and another in the overtime.
Quarterback Ryan Mallett completed 15-of-36 passes for 202 yards with one touchdown, and wide receiver Jarius Wright gained 90 yards on four receptions for the Razorbacks (8-5), who recorded their first bowl victory since a 27-14 decision against Missouri at the 2003 Independence Bowl.
ECU quarterback Patrick Pinkney, a fifth-year senior, completed 17-of-33 passes for 212 yards, one touchdown and two interceptions.
Dominique Lindsay rushed for 147 yards on 33 carries for the Pirates (9-5), who had won six of seven.