The 33-year-old Red Bull driver took full advantage of other people’s problems, including those of his 23-year-old German teammate Sebastian Vettel, to produce an assured drive that brought him his fourth win of the season and the sixth of his career.
Webber finished the 70-lap race 17.821secs ahead of Spain’s two-time champion Fernando Alonso of Ferrari with Vettel, hampered by a drive-through penalty for infringing the safety car rules, finishing a frustrated and angry third in the second Red Bull at the Hungaroring.
Webber’s win lifted him to 161 points in the title race and ahead of Britain’s 2008 champion Lewis Hamilton of McLaren, who was forced to retire with gearbox problems, on 157 points.
Vettel is now third on 151 with defending champion and team-mate Jenson Button fourth overall on 147 points.
Brazilian Felipe Massa finished fourth for Ferrari on the circuit where last year he suffered serious head injuries after a horrifying crash with Russian Vitaly Petrov grabbing his career-best finish in his rookie season in fifth place for Renault.
Another rookie, German Nico Hulkenburg, did the same by taking sixth place for Williams ahead of Spaniard Pedro de la Rosa of Sauber and Button, who came home eighth for McLaren.
Flying Japanese Kamui Kobayashi, who started on the back row, was ninth in the second Sauber and Brazilian veteran Rubens Barrichello, 38, claimed the final point in 10th place for Williams after surviving a dangerous barge by Michael Schumacher.