Kelechi Iheanacho's deft finish was ruled out by the assistant referee for offside against the Leicester striker in the 77th minute, only for the decision to be overturned and the goal given by the on-field referee about 70 seconds later on the advice of the VAR.
That second goal for Iheanacho clinched a 2-0 win for Leicester over third-tier Fleetwood at King Power Stadium, in one of five third-round replays.
The use of VARs is being trialed in England in the two cup competitions — the FA Cup and the League Cup — this season, but not yet in the Premier League.
"For this decision, I like (the use of) technology, of course," Leicester manager Claude Puel said, laughing. "It's a good thing ... the time was not so long to take the video and take the decision. That was the good thing."
West Ham needed extra time to see off third-tier Shrewsbury 1-0 at home, with 21-year-old Reece Burke smashing a shot in off the crossbar in the 112th minute. It took more than three hours for West Ham to score against Shrewsbury, with the original match finishing 0-0.
In other results, second-tier Cardiff earned the right to host Premier League leader Manchester City in the fourth round after beating fourth-tier Mansfield 4-1. Sheffield Wednesday beat Carlisle 2-0 and will next play Reading, which won 3-0 at home to Stevenage.
Chelsea, Swansea and Bournemouth are Premier League teams facing lower-league opposition in replays on Wednesday.