Rangers followed up their 4-0 triumph over Shamrock Rovers on Saturday with a second clean-sheet victory, this time over the League of Ireland’s bottom club at Lissywollen.
Summer signing Steven Caulker started in central defence, as Redknapp fielded a 5-3-2 formation which included Shaun Wright-Phillips at left wing-back.
Championship play-off final goal hero Zamora opened the scoring with a close-range finish in the first half after being set up by Wright-Phillips.
It was Zamora who assisted his strike partner Austin to double the Rs’ lead early in the second period.
Rangers complete their pre-season friendly programme with a home clash against Greek outfit PAOK on Saturday, with Hull City the visitors to Loftus Road on the opening day of the new Premier League season a week later.