Lampard handed the league leaders victory from the spot, firing home after referee Graham Poll decided Alexei Smertin had been brought down by Ledley King after 38 minutes.
But the award was hugely controversial, with Spurs claiming - convincingly - that King won the ball and Smertin simply went over his leg.
Whatever the verdict, however, Chelsea showed great steel to keep their rivals at bay and clinch victory with a second goal from Lampard when he drilled home from 18 yards in injury time.
It means Tottenham still haven't beaten Chelsea in the league at White Hart Lane for 18 years, but they probably started the brighter in a first half in which Lampard and Michael Carrick ran the show.
Erik Edman struck an excellent shot over the bar for the home side in only the second minute, while Robbie Keane headed narrowly wide when a Jermain Defoe cross deflected his way at the far post.
But Chelsea were in determined mood after hearing title rivals Manchester United had won 1-0 at Liverpool earlier in the day.
It meant the title race was right back on and that three points was crucial for Chelsea at White Hart Lane.
With John Terry dominant at the back they took their time getting into the game but soon showed glimpses of why they are top of the league.
Didier Drogba came agonisingly close to putting them ahead when he raced on to a Terry ball down the line and beat the offside trap.
His pace allowed him to reach the ball before keeper Paul Robinson, who had raced out of his goal. But he lofted his shot narrowly past the post.
Robinson made up for his rush of blood a few minutes later when Damien Duff turned sharply in the box and shot left-footed from 12 yards. The effort looked destined for the net, but Robinson flung himself to his left and kept it out with a two-handed save.
At the other end, Defoe also tested keeper Petr Cech with a vicious shot that swerved in the air and was only just parried to safety by the Chelsea man.
But two penalty claims proved crucial in the first half, and eventually Chelsea eased ahead.
The first appeal came when Arjen Robben fell under challenge from Noe Pamarot, but referee Poll decided he had simply toppled over.
But the second proved more fruitful and even more controversial for the visitors.
There were 37 minutes on the clock when Duff did superbly to keep the ball in play right by the corner flag and having slid in he turned to send a perfect pass for Smertin, who was racing into the box.
King spotted the danger and just got to the ball first, but Poll thought otherwise and awarded a spot-kick, that was confidently converted by Lampard.
The decision infuriated Spurs, who began the second half brightly and in determined mood. But still defenders remained on top, with Terry and King outstanding and even Noureddine Naybet making a crucial tackle on Drogba when he had raced through the middle and was set to shoot.
Tottenham came agonisingly close to equalising after 59 minutes, however, when Defoe took a corner on the left and sent it in low to the near post.
The ball bounced off Smertin's thigh and deflected high into the air, only just clearing the far post and the bar by a couple of inches.
With Chelsea so confident in defence, Tottenham realised they were going to need either something special or a little bit of luck to break their rivals down, and it seemed like their chance had come and gone.
But Spurs boss Martin Jol wasn't ready to give up and astonishingly moved King up front for the final 20 minutes after bringing on Anthony Gardner at the back.
He also brought on youngster Dean Marney to try and open up Chelsea and the changes certainly livened things up.
With King causing problems in the air there was a new verve to Tottenham's attack and Chelsea knew they were in for a battle.
Both Keane and Pedro Mendes blasted shots well wide, but Tottenham couldn't fashion a clear-cut chance and Chelsea sealed victory when substitute Eidur Gudjohnsen set up Lampard to fire home from the edge of the box in time added on.
Man of the Match: Frank Lampard - The England midfielder was again a pivotal figure for the Blues and netted both goals to keep them on track for league success.