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Redknapp's charges began the brighter, with Austin, in particular, proving the most likely candidate to open the scoring after seeing his 11th-minute header tipped over the crossbar by goalkeeper Lee Camp.
The 24-year-old would not be denied a second time, though, as the former Burnley hitman poked past Camp from close range to score in his third successive fixture.
There was a moment of controversy on the half-hour mark, as Tommy Elphick appeared to use his hand to deny Austin a clean sight goal but, much to the fury of the home supporters, no card was issued for the defender.
The hosts had not scored more than once in any of their three previous games in England's second tier, but Hoilett brought an end to that record early in the second half, firing past Camp from a tight angle to establish daylight in the scoreline.
Phillips secured the points with 13 minutes remaining, racing through on goal before smashing past Camp as the capital club registered an impressive victory.