Wycombe took the lead on 13 minutes when Ian Stonebridge saw Phil Smith off his line, and lobbed him from 35 yards with the ball just dipping below the bar and into the net for a goal of the season.
Swindon came close a few more times, but both sides went into the half time break with Wycombe still leading 1-0.
Pook and Onibuje came on at half time replacing Weston and Brownlie.
Swindon came close again with Onibuje's header going just wide, and Smith had to make a couple more saves to prevent Wycombe from scoring, but Swindon ran out of time and Wycombe won 1-0 to go into the second round of the Johnstone's Paint Trophy.
Overall an uneventful game when a fluke goal won it for Wycombe, with neither side looking very good. Only 1,583 watched the game with 368 coming from Swindon. Swindon now travel to Shrewsbury on Saturday in league action.