The easy win left England - who failed to qualify for the 2008 European Championships - 10 points clear of Croatia at the top of Group Six.
Rooney's goals took his tally to eight in England's seven qualifying matches.
The mismatch against the Pyrenean principality - ranked 196 in the world - saw England take a very comfortable step towards qualification in their final game of the season.
Despite a strike on the London Underground train network that left many supporters stranded, some 57,897 people watched the game - a figure nonetheless approaching that of the entire Andorran population.
In changes to the team that beat hosts Kazakhstan 4-0 in Almaty on Saturday, David Beckham earned his first England start under manager Fabio Capello - and a national outfield record-extending 112th cap - in place of the suspended Gareth Barry in central midfield.
Andorra, beaten 2-0 by England in Barcelona in the opening group game last September, played a 5-4-1 formation in a bid to keep the hosts at bay.
Rooney twice exposed Andorra goalkeeper Koldo Alvarez inside the first three minutes.
The visitors' captain - in his 78th and final international - tipped an attempted chip over his crossbar and seconds later, having parried a Theo Walcott shot, saw the Liverpudlian head a rebound against the bar.
Right-back Glen Johnson's cross found Rooney completely unmarked in the penalty box and the striker directed a simple header across Alvarez to open the scoring.
Andorra succeeded in keeping England at bay until Chelsea midfielder Lampard made it 2-0 thanks to some excellent work on the right flank from Johnson and Walcott.
The Portsmouth defender played in Walcott who cut the ball back to Lampard, unmarked as he swept into the penalty box.
Rooney sidefooted in his second goal following a pinpoint cross to his feet from man-of-the-match Johnson.
Capello replaced Rooney with Tottenham striker Defoe and Gerrard with Ashley Young at half-time.
The members of England's 1966 World Cup-winning squad who did not play in the final were paraded during the interval, having been presented with FIFA winners' medals by British Prime Minister Gordon Brown earlier on Wednesday.
Defoe screwed an early chance across the face of goal, while Lescott failed to connect with a Beckham cross as England initially struggled to extend their lead.
Defoe eventually got off the mark, leaping to head in another Johnson cross following a Beckham corner.
And two minutes later he tapped in the rebound after Alvarez spilled a Beckham free kick.
The tiring visitors conceded a shambolic goal 10 minutes later, with two defenders and the goalkeeper failing to clear the ball after a Defoe shot and Crouch tapping in England's sixth.
England face second-placed Croatia here on September 5. However, England could have already qualified for South Africa by then, should Croatia fail to win in their two early season matches against Belarus.
Source: AFP European Edition