An error by Liverpool captain Steven Gerrard handed Drogba a simple opening goal in the first half and Lampard added a second after the break.
The result ensured Chelsea remained in pole position to win their first championship for four years but also finally put paid to the Merseysiders' hopes of securing Champions League football next season.
With Manchester United a point behind before kick-off and playing later in the day, Carlo Ancelotti's side knew anything less than a win would hand the initiative to their rivals.
And with next week's final weekend seeing United host Stoke - Chelsea are at home to Wigan - there was no margin for error.
Chelsea were undoubtedly the better side but the match may have turned out differently had they not been gifted a 33rd-minute lead.
The conspiracy theorists would certainly have had a field day.
Some fans had been suggesting all week they would rather Chelsea win an Anfield than beat the Stamford Bridge side and hand United the chance to eclipse the club's tally of 18 league titles.
However, even they could not have prophesied the manner of Chelsea's goal.
Gerrard failed to notice Drogba when he passed back to Jose Reina and the Ivory Coast international nipped in to round the goalkeeper and tuck the ball home.
Prior to that, the early exchanges had been open. Lampard shot wide and Nicolas Anelka forced Reina into a low save while Liverpool's Maxi Rodriguez and Javier Mascherano, standing in at right-back because of Glen Johnson's calf injury, saw shots deflected wide.
There were also three penalty claims in what was a bustling first half.
Two for Chelsea involved Salomon Kalou and his tendency to hit the ground as soon as he entered the box.
His first was a blatant dive in the ninth minute under Mascherano's challenge but referee Alan Wiley allowed that to go unpunished.
In added time at the end of the first half the same player was through on goal - with Lucas Leiva in close attendance - and managed to trip himself up.
Despite fierce Chelsea protests Wiley again made the correct decision.
Whether he got Alberto Aquilani's 26th-minute penalty shout right was open to debate after the Italy international went down under Branislav Ivanovic's challenge as he raced on to Rodriguez's chipped pass was open to debate as the defender appeared not to get the ball.
The loss of Rodriguez to injury just before half-time, when he was replaced by Ryan Babel, was a blow to Liverpool.
Six minutes into the second half Kalou muscled his way past Mascherano to drill a cross into the six-yard area, where Anelka failed to get the touch which would certainly have brought a second Chelsea goal.
But the Frenchman played a more influential role in the 54th minute when his cross picked out Lampard who bundled home from close range.
If that was not bad enough for Liverpool, they then lost Carragher to injury which meant 19-year-old Daniel Ayala was thrust into the action.
A forlorn-looking Fernando Torres, whose season was prematurely ended by a second knee operation in three months, could only watch on despondently from the stands.
It would have been 3-0 in the 67th minute had it not been for Reina's one-handed save from Florent Malouda's low shot.
David Ngog replaced Aquilani for the final 15 minutes but Liverpool were a spent force with only Reina keeping Chelsea at bay, punching away Michael Ballack's 25-yard free-kick and then producing a smart double save from Anelka and then Kalou.
The defeat meant Liverpool will finish the season with their lowest points total in five years, since accruing 58 in Rafael Benitez's first campaign in charge back in 2004-05.
Whether the Spaniard, strongly linked with Juventus, is around next season to rectify that remains in doubt.
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