Sebastian Vettel was 5.1 seconds behind Alonso in third for Red Bull, ahead of McLaren duo Lewis Hamilton and Jenson Button. VettelÃ¢â‚¬â„¢s team-mate Mark Webber was sixth, after losing out at the pit stops, and nursing an oil-consumption problem.
The result was FerrariÃ¢â‚¬â„¢s second one-two of the season, but their first race win since Alonso won in Bahrain.
Alonso and Massa both got off the line well to get past pole-sitter Vettel, but it was Massa who led for the majority of the race.
Alonso was heard to complain on the radio that he could not get past his team-mate calling the situation Ã¢â‚¬Å“ridiculousÃ¢â‚¬Â before backing off.
MassaÃ¢â‚¬â„¢s race engineer Rob Smedley was then heard to say: Ã¢â‚¬Å“Alonso is quicker. Can you confirm you understand?Ã¢â‚¬Â then after Alonso went through saying Ã¢â‚¬Å“Good lad. Stick with it now. Sorry.Ã¢â‚¬Â
Smedley again commented on the move following the raceÃ¢â‚¬â„¢s conclusion, calling his man Ã¢â‚¬Å“magnanimousÃ¢â‚¬Â for pulling over for Alonso.
Within seconds of the move, cries of foul play rippled around the internet as fans on Twitter condemned the move similar to the one Ferrari deployed in Austria 2002 to hand Michael Schumacher the win.
The move is in contravention of Rule 39.1, prohibiting team orders which interfere with a race result and Ferrari were later fined $100,000 for breaching sporting regulations.
Ferrari team principal Stefan Domenicali denied allegations of team orders in post-race interviews, but Red Bull rival Christian Horner was adamant that the coded message from Smedley, and the unexpected decrease in speed from Massa was deliberate.
Massa said later that Ã¢â‚¬Å“he passed meÃ¢â‚¬Â, but the evidence would suggest an order was made and he let his team-mate through.
Elsewhere, Michael Schumacher finished eighth on his return to his home grand prix, while Mercedes team-mate Nico Rosberg could only manage ninth quickest despite out-qualifying Schumacher.
Robert Kubica took seventh for Renault with team-mate Vitaly Petrov finishing 10th as the top five teams in the world championship locked out the top 10.
SauberÃ¢â‚¬â„¢s Kamui Kobayashi was unable continue his recent points-scoring form as he finished 11th ahead of the WilliamsÃ¢â‚¬â„¢ of Rubens Barrichello and Nico HÃƒÂ¼lkenberg.
Virgin Racing were the best of the new teams as Timo Glock took 18th after Heikki Kovalainen retired on the penultimate lap for Lotus with both cars failing to complete the race.
Bruno Senna, recently returned to the cockpit after his demotion at Silverstone, finished 19th and last as the only HRT driver to complete the race.
Despite only finishing fourth, Hamilton continues to lead the world championship with 157 points ahead of team-mate Button with 147.
Webber and Vettel are now equal third, while Alonso closes to just 34 points behind.
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