Aaron Lennon scored his first goal for Tottenham to set them on their way back into the top four, but Birmingham's relegation worries have deepened.
Keane scored his 11th goal of the season to seal victory
Lennon scored with his left foot after collecting a cross from Jermain Defoe.
Robbie Keane sealed victory with a close-range finish, tapping home a cross from Jermaine Jenas.
Birmingham impressed in the first half but created little, while Maik Taylor saved from Defoe and Nicky Butt blocked a Michael Dawson shot.
Arsenal's home win over Charlton earlier on Saturday had led to them briefly moving above Tottenham in the Premiership table as the scramble for Champions League qualification intensifies.
But Tottenham are now two points clear of the Gunners with eight games remaining.
It was a miserable afternoon for Birmingham, who remain third from bottom.
Fellow strugglers West Brom, one place above Birmingham, lost to Manchester United, but Porstmouth defeated West Ham to move level on points with Steve Bruce's team.
The match had started promisingly for Blues, who set about Tottenham with great enthusiasm.
The lively DJ Campbell, making his first Premiership start, just failed to make the crucial touch on a low Emile Heskey cross, while Nicky Butt headed a free-kick wide.
Two more openings came Heskey's way but he was let down by a heavy touch and then a mis-timed shot.
Michael Carrick had struck a low free-kick that Maik Taylor saved in the opening minutes.
Tottenham created no further chances until just before the break, when Melchiot came to Birmingham's rescue with a brilliant tackle to deny Keane.
Lennon had fed Jenas down the right and his early low cross found Keane with only Taylor to beat but, as the Irishman shaped to shoot, Melchiot hooked the ball out of play.
Spurs carved out the first opening of the second half, Defoe latching on to a header from Keane and forcing a finger-tip save from Taylor.
From the subsequent corner Dawson shot powerfully at goal and the ball appeared to strike Butt on the arm two yards in front of goal but referee Uriah Rennie turned down Tottenham's penalty appeals.
After their bright start, Birmingham started to look increasingly unsure, while Heskey limped off to add to the club's lengthy injury list.
Lennon put Tottenham in front with a left-foot strike that nestled in the bottom corner after collecting a cross from Defoe and cutting inside Jamie Clapham.
Defoe had dispossessed Melchiot at the start of the move and the defender was booed by his own fans afterwards.
Keane sealed victory with his 11th goal of the season.
Birmingham City manager Steve Bruce:
"Up until the first goal the players have given us everything. They were at full tilt.
"The kick in the teeth is the hideous mistake for the goal. All week we have talked about the basics and against Spurs a mistake like that is game over.
"You could see the confidence drain out of players after that."
Tottenham head coach Martin Jol:
"Birmingham have a good home record. We knew it would not be easy and the first half was very scrappy.
"In the second half we did well and I am especially pleased for the younger players. Ledley King and Michael Dawson were terrific at the back.
"Aaron Lennon, only 18, showed great composure with his left foot, which is not his strongest, for his goal."
Birmingham: Maik Taylor, Melchiot, Martin Taylor, Cunningham, Clapham, Pennant, Johnson, Butt, Lazaridis (Kilkenny 81), Heskey (Forssell 57), Campbell.
Subs Not Used: Vaesen, Clemence, Tebily.
Booked: Cunningham, Butt.
Tottenham: Robinson, Kelly, King, Dawson, Lee, Lennon, Carrick, Davids, Jenas, Keane (Murphy 78), Defoe.
Subs Not Used: Cerny, Tainio, Mido, Gardner.
Goals: Lennon 65, Keane 77.
Ref: U Rennie (S Yorkshire).