The midfielder's first appearance was against Arsenal as Championship side Rovers caused the shock of the fifth round at the Emirates on Saturday.
David entered the fray at 0-0 with 62 minutes on the clock and 10 minutes later, Colin Kazim Richards struck the only goal of the game.
David may now come face-to-face with Spurs team-mate Adam Smith for a place at Wembley in the semi-finals.
Adam came on as a late substitute as Millwall beat Luton Town 3-0 in Saturday's early kick-off and the Lions now host Rovers in the quarter-finals.
Jordan Archer started as Wycombe lost 1-0 at Bristol Rovers in League Two.
Heurelho Gomes made a number of fine saves to no avail as Hoffenheim suffered a 1-0 defeat at home to Stuttgart in the Bundesliga.
Yago Falque played 90 minutes as Almeria drew 2-2 against Guadalajara in Spain's Segunda Division. Almeria stay second, but are 12 points adrift of Elche.
In Italy, Souleymane Coulibaly came on in the 61st minute as Grosseto scored a last-minute equaliser in a 2-2 draw against Lanciano in Serie B.
Bongani Khumalo came off the bench at the start of the second half as PAOK draw 0-0 against AEK in the Greek Super League. PAOK slip to third and are 17 points behind leaders Olympiacos.