The Spurs striker, returning to the starting line-up after injury, netted against his former side as Spurs reacted perfectly after the sacking of boss Glenn Hoddle.
The Republic of Ireland international followed fellow striker Freddie Kanoute on to the scoresheet as Tottenham, under the control of David Pleat, had the game won inside the first half an hour.
Coventry had started well enough without posing much of a threat but then, after 13 minutes, Kanoute picked up a pass from his strike partner and raced clear of the flat-footed Coventry reargurard.
Scott Shearer came racing off his line but the Frenchman beat him coolly.
The home side could have pulled level four minutes later when Dele Adebola moved on to a long forward pass from Mo Konjic, beat Anthony Gardner and flicked the ball over Kasey Keller.
The effort lacked power, but was heading for the net before Dean Richards hooked it clear.
Spurs did not have to wait long, however, for their second. Konjic slipped at the crucial time to allow Keane to win possession just outside the area. Steve Staunton managed to retreat and cover, but Keane turned him twice before finishing with a left-foot shot into the corner of the net.
Only Shearer prevented the visitors from notching a third when he made a fine double save to deny Gus Poyet.
Coventry made two changes at half time, bringing on Claus Jorgensen and Graham Barrett and they gave a better account of themselves.
The Dane, signed on a free from Bradford, slotted in on the left and supplied the width they had so painfully lacked in the first half.
Adebola continued to work hard and Gardner and Richards a surprisingly tough time, but Spurs did not have to over-exert themselves to make it through to the next round.
Their passage was made that much easier when sub Rohan Ricketts hammered home a stunning 25-yard effort which went in off the bar.
Coventry: Shearer, Shaw, Konjic, Staunton, Warnock, Mansouri, Suffo, Safri, Doyle, Adebola, Morrell. Subs: Arphexad, Whing, Barrett, Jorgensen, Davenport.
Tottenham: Keller, Carr, Bunjevcevic, Gardner, Richards, Taricco, Anderton, Poyet, Blondel, Kanoute, Keane. Subs: Postiga, Dalmat, Doherty, Burch, Ricketts.
Referee: M Jones (Cheshire)