The tactic appeared to be working in a dull first half until Keane struck on the stroke of half-time, heading home from close range after good work from Landon Donovan.
Keane turned creator with a fine ball out wide to Sean Franklin whose low cross was driven home by Mike Magee to make it 2-0 in the 64th minute.
The Donovan-Keane combination bore fruit again three minutes later with the American breaking down the left and his deflected shot was turned goalwards by Swede Christian Wilhelmsson with Keane adding the final touch.
Despite their handsome lead, Keane, who wasn't picked for Ireland's friendly with Greece on Wednesday so he could concentrate on the MLS playoffs, said: "We had a wonderful night, but we know anything can still happen. It's not over."