A long throw into the box was knocked to the 37-year-old by Joe Corona, with the Swede taking a couple of touches before finding the net with a spectacular strike.
But the 84th-minute goal, his 11th of the season, was too late as New England held on to remain undefeated in four games.
Cristian Penilla had opened the scoring just before half-time as his fierce shot crept through the hands of keeper David Bingham.
New England’s lead was doubled on the hour mark when Teal Bunbury slotted into the net after being put through by Carles Gil.
Ibra’s goal was the pick of the bunch at the Dignity Health Sports Complex but the Galaxy could not make their late pressure count.
Elsewhere, Auston Trusty kept his cool to convert a late chance as the Philadelphia Union beat Minnesota United 3-2 to maintain their top spot in the Eastern Conference.
Minnesota had the bulk of the early chances, but Philadelphia were first on the score sheet when Jamiro Monteiro buried an 18th-minute penalty.
Hassani Dotson drew the Union level 10 minutes later, but Haris Medunjanin ensured the visitors finished the half up 2-1 with a deft free-kick one minute before the break.
Kevin Molino drew the game level at 2-2 on 77 minutes, but second-half substitute Trusty was first to a deep cross from fellow replacement Ilsinho to score and deal Minnesota their first home defeat at Allianz Field.
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