The ad, created by Abbott Mead Vickers BBDO, was shown for the first time during yesterday's (15 April) FA Cup semi-final between Chelsea and Tottenham on ITV.
It will air until 12 May, and between 27 May and 23 June, and also features England footballers Theo Walcott, Glen Johnson and Scott Parker. The campaign will also run across press, outdoor, PR and digital.
As part of the campaign, Mars is giving away 100,000 "official special-edition" England shirts through an on-pack promotion.
The ad is set around a tense England penalty shootout with the Premier League's top goal-scorer Van Persie getting ready to take a penalty as England's keeper is carried off the pitch with a knee injury.
Walcott, Johnson and Parker look on, dejected, knowing they need a minor miracle to keep the Arsenal hit man from scoring.
Meanwhile, realising England are in trouble, one of the stewards takes a bite of his Mars bar before stripping off his jacket and taking his place between the posts. Inspired, he plucks Van Persie's penalty out of the top-right corner.
The new-found hero saves another penalty, sees one penalty miss, and is then mobbed by the other England players.
The showing of the ad comes ahead of this year's European Championship, taking place in Poland and Ukraine between 8 June and 1 July.
Mars is an official sponsor of the Football Association (FA), the sport's governing body, having signed a five-year deal in 2009.
Follow John Reynolds on Twitter @johnreynolds10