Meanwhile, leaders Manchester United stretched their lead over second-placed Arsenal - who play Sunday - to 17 points after beating Leicester City 2-0 thanks to goals in the last two minutes of action from Ole Gunnar Solskjaer and Mikael Silvestre.
Ipswich Town consolidated third place with a 1-0 win at West Ham, Leeds United moved up into fifth with a 2-1 win at Charlton Athletic and 10-man Middlesbrough aided their survival bid with a 2-1 win at local rivals Newcastle United.
Two goals by Don Hutchison saw Sunderland beat Chelsea 4-2.
The new Spurs era kicked off in frantic fashion at White Hart Lane.
Spurs went ahead in the 29th minute when Stephen Clemence whipped in a corner kick and Stefan Iversen rose unchallenged to head home the opening goal.
If Coventry manager Gordon Strachan was unhappy with his defence for the first goal his mood did not improve five minutes later.
Referee Graeme Poll penalised City for a seemingly innocuous challenge by David Thompson on Luke Young and from the resulting free kick Spurs were two ahead. Again Clemence picked out Iversen, whose header was saved by Chris Kirkland but Les Ferdinand was on hand to poke home from close range.
The second half started quietly with play mainly condensed into the middle of the park, but Spurs ended the game as a contest in the 59th minute.
Ferdinand switched play to the left before Ledley King picked out Sergei Rebrov with a superb pass. The Ukrainian star slotted the ball past Kirkland to the delight of the Spurs' fans.
The result was the perfect tonic for Spurs after the shock sacking of Graham on Friday, but Strachan's Coventry woes continue.
Leeds moved up to fifth in the Premiership after goals from Mark Viduka and Alan Smith saw them complete the double over Charlton with a 2-1 win.
Shaun Bartlett had pulled his side back into the game with a first half leveller before Smith struck the eventual match-winner immediately after the re-start.
Both sides had gone into the game with good records since the turn of the year. Alan Curbishley could boast an unbeaten Premiership run while David O'Leary's men had picked up 13 points from the last 15 on offer away from Elland Road.
And it was Leeds who got off to a dream start when Australian Viduka converted Ian Harte's left-wing cross after just 11 seconds with a shot that found its way into the bottom right-hand corner of Sasa Ilic's net.
It was the Australian international's fourth goal in four games, and third of the campaign against Charlton.
The Londoners were back on terms after 18 minutes though when Bartlett grabbed his fifth goal in the last ten games.
Viduka was booked for a foul on Scott Parker and from the free- kick Richard Rufus found Bartlett, who managed to beat an advancing Nigel Martyn to the ball and head the hosts back into the game.
Leeds started the second half as they had begun the first when Smith fired the visitors back into the lead. The Whites broke from the edge of their own box and advanced the length of the field before Smith made no mistake to beat Ilic.
The result sees Charlton slip to only their second home league defeat this season although they remain in tenth place in the Premiership table.
(kil/dpa)