The 29-year-old Spaniard, winner of the British race for Renault in 2006, secured Ferrari's first win since last year's Korean Grand Prix with a controlled drive - and some luck - to exploit the controversial revised technical regulations.
It was Alonso's 27th career victory, drawing him alongside three-times champion Briton Jackie Stewart in the record books.
And it came on an afternoon of high drama that saw defending champion and runaway leader Sebastian Vettel's race undone by a slow pit-stop.
Vettel finished second ahead of his Red Bull teammate and pole setter Mark Webber, with McLaren's home favourite Lewis Hamilton in fourth after a superb rousing race. Red Bull used team orders to stop Australian Webber passing Vettel on the final lap.
"Hold the gap, maintain the gap, keep station," the Red Bull team told Webber, last year's winner. Team chief Christian Hornder said Webber respected that order.
Vettel, who crossed the line over 16 seconds behind Alonso, retained his lead in the drivers' championship on 204 points from Webber on 124 with Alonso moving up into third on 112.
"A fantastic day, fantastic day," said a delighted Alonso on the team radio during the slowing down lap.
"A great win," said Ferrari team chief Stefano Domenicali.