The USA striker hit the all-important opener in the 12th minute as we got the job done in the first half at the Lane.
Dempsey finished from close range to settle the team down and a quickfire double from Gareth Bale and Dempsey's second sealed it at 3-0 by half-time.
Andre Villas-Boas made seven changes to the team that started against Reading on New Year's Day.
Most notably, Scott Parker made his first start of the season and Benoit Assou-Ekotto was back for his first action since September.
Brad Friedel was back in goal, Bale back from suspension and Steven Caulker, Tom Huddlestone and Dempsey were all in the line-up.
On top from the off, Parker and Huddlestone had early sighters before the key early goal every Premier League side craves in these cup ties.
Gylfi Sigurdsson was dragged down on the right, picked himself up and curled in a free-kick that Bale flicked on for Dempsey to provide the finish from close range, 14 minutes on the clock.
Bale fizzed in a cross that somehow evaded everyone, Kyle Naughton tested Joe Murphy down to his left and then Bale took off on a typical run, charging past five Coventry players before planting a shot agonisingly inches wide.
It wasn't long before Bale hit the target. Dempsey tried his luck from the edge of the box, his shot looped up off William Edjenguele and Bale stetched to volley home at the far post for 2-0.
The pair combined again for 3-0 on 38 minutes and it couldn't be easier, Bale's deep corner met by Dempsey, who looped his header back over Murphy and into the far corner.
Coventry's only threat came when Naughton did well to touch Jordan Clarke's cross away from Leon Clarke, with Steven Jennings firing the loose ball wide.
Dempsey hit a spectacular dipping volley just before half-time as he chased his first Spurs hat-trick.
Caulker had the first chance of the second half, but appeared to slightly mistime his header from Huddlestone's free-kick.
Bale was upended on the edge of the box on the hour and left Murphy rooted to the spot from the free-kick, his effort drifting inches wide.
Friedel had to be alert to keep out Edjenguele's header on 67 minutes but play was soon down the other end as Bale charged into the box and forced Murphy into a fine save down to his left.
That was Bale's last action as he was replaced by Andros Townsend on 71 minutes. Mousa Dembele and Tom Carroll then came on for Parker and Sigurdsson.
Into the last 10 minutes and Townsend had his usual impact, firing just wide on two occasions, with Dempsey just off target from a 20-yard free-kick, his final chance of that treble.
Spurs (4-4-2): Friedel; Naughton, Caulker, Dawson, Assou-Ekotto; Sigurdsson (Carroll, 80), Huddlestone, Parker (Dembele, 80), Bale (Townsend, 71); Adebayor, Dempsey. Unused subs: Lloris, Vertonghen, Lennon, Defoe.
Coventry City (4-4-1-1): Murphy; J Clarke, Wood, Edjenguele, Adams; Baker, Bailey (Thomas, 59), Jennings (Fleck, 71), McSheffrey; Moussa (Barton, 51); L Clarke. Unused subs: Dunn, Cameron, Elliott, Christie.
Goals: Spurs - Dempsey (14, 38), Bale (33).
Yellow cards: Coventry City - Bailey, Baker.
Referee: Mr M Naylor.