However, the winger's match-winning efforts didn't distract from another lacklustre display from Fabio Capello's side. England laboured through a poor first half at Barcelona's Olympic Stadium before Cole came on to score two well-taken goals in the space of seven minutes.
There was never any real doubt the visitors would leave Spain with three points, but the way they struggled to break down Andorra's collection of part-time players will be a major concern for Capello ahead of the crucial clash against Croatia in Zagreb.
"People think that this should be an easy game but they got 10 men behind the ball and made it difficult on a very sticky pitch," said Cole. ".
"No we have to move on and face Croatia. The two games are different animals, you can't compare them."
The Italian gave Theo Walcott his first start in place of David Beckham as he tried to give England an injection of pace. Glen Johnson came in at right-back ahead of Wes Brown, while Joleon Lescott replaced injured centre-back Rio Ferdinand and Jermain Defoe partnered Wayne Rooney up front.
Andorra included an insurance salesman and a painter in their side, but the players of the tiny principality, 186th in FIFA's world rankings, had rattled England during their last meeting in March 2007. A far more convincing performance was essential to provide a confidence boost before the Croatia game but England couldn't deliver.
There was early optimism as that extra speed down the flanks almost paid dividends in the first minute when Walcott surged clear and crossed towards Defoe, only for Koldo to smother the loose ball. Walcott threatened again two minutes later when he ran onto Rooney's pass and chipped his shot over from a tight angle.
With Andorra content to defend with as many as nine players whenever England crossed the halfway line, it was essential Capello's side maintained a high tempo. But they too often let the game drift and lacked the wit to deliver the killer pass that would unlock Andorra's massed defence.
Walcott's flick gave Rooney a golden opportunity in the 17th minute, but the Manchester United star's tentative finish was in keeping with his poor goal-scoring record for England.
Although Frank Lampard flashed a powerful low strike just wide moments later, the first signs of discontent from the England fans were heard as passes went astray with alarming regularity. Gareth Barry scuffed a close-range effort wide before half-time and, for the second time in 18 months against the Andorrans, England trudged off to a chorus of disapproval.
They hadn't forced Koldo to make a proper save in 45 minutes and Capello was quick to show his anger by sending his players out early for the start of the second half. More significantly he put on Emile Heskey for Defoe and Cole for Stewart Downing. It had taken Steve McClaren's England 54 minutes to score against Andorra. At least Capello avoided the ignominy of breaking that record as Cole struck in the 48th minute.
Lampard floated in a free-kick that deflected off Lescott to Cole and the substitute lashed his volley past Koldo. Cole had given England the dynamism they lacked in the first half and he scored again in the 55th minute.
Rooney provided the assist with a perfect pass and Cole ran through to clip his shot into the net. Cole thought he had a hat-trick when he turned in Johnson's shot but the effort was ruled out for offside.