Lampard and Didier Drogba hit the woodwork for Chelsea before the striker was sent off in extra-time for slapping United defender Nemanja Vidic.
Ronaldo missed his penalty for United, but John Terry hit the post and Edwin van der Sar saved from Nicolas Anelka.
It sparked wild celebrations for Sir Alex Ferguson and his players in the Moscow rain as United lifted Europe's major club trophy 50 years on from the Munich air crash and repeated their previous successes in 1968 and 1999.
Chelsea captain Terry had to be consoled by boss Avram Grant as he broke down in tears on the touchline after missing the penalty that would have given his side the trophy, crucially slipping in his run-up on the treacherous rain-sodden turf and sending his kick against the upright.
The opening exchanges amounted to little more than sparring - but the game burst into life after 20 minutes after an aerial collision between Paul Scholes and Claude Makelele that left both players with a yellow card and the Manchester United veteran with a bloody nose.
It opened the way for a passage of play that made a mockery of predictions that this would be a dour encounter in the mould of their 2007 FA Cup Final encounter.
Ronaldo had been giving Essien a torrid time, and his threat was transformed into tangible results after 26 minutes when he soared above the Chelsea defender to meet Brown's cross and head his 42nd goal of the season and put United ahead.
Chelsea were almost gifted an equaliser in bizarre circumstances seven minutes later when United keeper Edwin van der Sar was forced to claw away a header from his own defender Rio Ferdinand after Didier Drogba forced Frank Lampard's cross into the six-yard box.
Cech somehow denied Manchester United a second in the 34th minute after a stunning move that swept from one end of the field to the other in an instant and left Chelsea exposed.
Wayne Rooney found Ronaldo with a raking pass, and his cross was delivered to perfection for Tevez, whose header was blocked by Cech - who then recovered to make a magnificent one-handed save from Carrick's follow-up effort.
Tevez was denied again four minutes before the interval when he escaped the attentions of Makelele but could not slide in Rooney's low cross.
United were left to regret their missed chances when Chelsea took advantage of several slices of good fortune to equalise on the stroke of half-time.
Essien's shot was speculative at best, but two crucial deflections off Nemanja Vidic and Ferdinand saw the ball fall kindly for Lampard, who slotted in a neat finish - and his celebration demonstrated that the goal was dedicated to the memory of his late mother Pat, who died in April.
Ronaldo's duel with Essien had been a mis-match, but the Ghanaian was more effective as an attacking driving force after 54 minutes when he finally turned the tables on his tormentor only to shoot narrowly over the top from 20 yards.
Chelsea had been transformed by the equaliser, and suddenly they were the team passing with purpose and looking the more likely side.
And the much-debated Luzhniki Stadium pitch was suddenly starting to exert an influence, with both Ferdinand and Lampard suffering from cramp.
Drogba had been a peripheral figure for much of the game, but he produced a moment of brilliance with 13 minutes left that almost put Chelsea in front when he curled a right-foot shot against the post from 25 yards.
There was a moment of history three minutes from the end of normal time when Ryan Giggs replaced Scholes to make his 759th appearance for United, beating the previous club record held by Sir Bobby Charlton, who was watching from the stands.
Chelsea boss Grant bizarrely left it until two minutes into extra-time to make his first change, sending on Salomon Kalou for the disappointing Florent Malouda.
The woodwork denied Chelsea again seconds later when a superbly disguised pass from Michael Ballack set up Lampard, but his shot rebounded to safety off the bar with Van der Sar beaten.
It was a compelling game, and United were left cursing 10 minutes into extra time when Chelsea captain Terry headed off the line miraculously from Giggs after Patrice Evra had shown pace and strength to fashion the opening.
Rooney had suffered a frustrating evening, and he looked less than satisfied when he was hauled off as United introduced the pace and unpredictability of Nani.
Drogba was sent off four minutes from the end of extra time by Slovakian referee Lubos Michel for slapping Vidic after an ugly melee developed when Chelsea felt Tevez and been unsporting in returning the ball after a break for players to be treated for cramp.
Tevez and Michael Carrick were on target for United as the shoot-out started, with Ballack and Juliano Belletti following suit for Chelsea.
Ronaldo then made a hash of his kick, stopping in his run-up before seeing his kick saved by Cech.
Lampard was again successful from the spot and Owen Hargreaves scored under pressure before Ashley Cole's penalty took Chelsea to the brink of victory.
Nani scored to prolong the tension, but with defeat staring United in the face, Terry threw them a lifeline with his miss.
Substitutes Anderson and Kalou traded successful kicks before Giggs threw all the responsibility on Anelka as the shoot-out reached sudden death - and it proved too much for the striker, who saw his penalty palmed away by Van der Sar to crown United as kings of European football once again.