Southampton went into the match with four successive wins behind them and needed only 100 seconds to go in front.
But the expected avalanche of goals never materialised as Rangers recovered to win with some ease.
Saints were watched by their biggest crowd of the season, 25,185, but they gave little value for money and can have no complaints about the result.
Southampton looked to be on course for a comfortable victory when Rudi Skacel crossed from the left for Jermaine Wright to score his first goal for the club with a mis-hit shot which appeared to deceive ex-Saints goalkeeper Paul Jones.
Jones prevented a second goal after 12 minutes when he dived to his left to the foot of the post to push away a fierce free-kick from Gareth Bale.
But that was as good as it got for Southampton and, even though they lost defender Matthew Rose to injury after 24 minutes, they gradually got on top.
Davis made a good save to deny Martin Rowlands before Rangers equalised in the 34th minute.
Dexter Blackstock was sold by Southampton only six weeks ago for £500,000 and it was almost inevitable that he should come back to haunt them.
Lee Cook was involved in the build-up down the left and his centre to the middle of the goal was met by a diving header from Blackstock for his third goal in Rangers colours.
Paul Jones made a good save from Skacel and a surging run by Bale ended with Jones saving under his bar from Grzegorz Rasiak.
Rangers delighted new manager John Gregory with a second goal after 38 minutes although Davis was heavily at fault.
The former Ipswich and Sunderland keeper raced to the edge of his area near the by-line to usher a ball out of play but allowed himself to be dispossessed by Ray Jones.
He did not have much of an angle to work with, but his low left-foot shot was stunningly accurate and Rangers celebrated while Davis hung his head in shame. In an earlier match this season Davis blundered when he allowed a free-kick from Preston's Simon Whaley to go through his legs for an equaliser.
Paul Jones made a couple of important saves in the second half as Southampton attempted to snatch an equaliser but the longer the match went on the less likely Rangers were to surrender their initiative or the lead.