Antti Niemi was in particularly impressive form for the Saints, producing top-quality saves to deny both Joleon Lescott and Kenny Miller.
His task was made all the more difficult when defender Claus Lundekvam was sent off for a second bookable offence late in the second half.
All the talk before the game was of both sides' potential title aspirations but neither team seemed willing or able to break the deadlock and get off to a flying start.
Saints included six new faces from the team that lined up against Manchester United in the final game of last season.
Polish international Tomasz Hajto made his debut alongside Darren Powell and Lundekvam in the Saints defence.
And hotly tipped youngster Kenwyne Jones was given a starting berth upfront with new boy Ricardo Fuller.
Wolves included their main summer acquisition, former Celtic man Jackie McNamara, in what was an impressive looking back four.
And it was the visitors who had the best of the first-half exchanges, as Mark Kennedy delivered two thunderbolt 25-yard efforts which Niemi did well to parry wide.
Lescott was also unlucky when he saw his free header tipped round the post by the Finnish international.
The introduction of Dennis Wise in the second half yielded a greater attacking threat for Southampton as his biting midfield display drove them forward.
Club captain Nigel Quashie saw a low left-foot drive well saved by Wolves keeper Michael Oakes and Fuller missed two glaring opportunities in the space of two minutes.
Lundekvam put pressure on the Southampton back line when he was given his marching orders for a cynical trip on Miller. Quashie and Wise were incensed though that an earlier Paul Ince challenge was not picked up by referee Trevor Kettle.
However, Harry Redknapp threw whiz kid Theo Walcott into the fray with 15 minutes to go but for all of his trickery, Saints still couldn't find a way past Oakes in the Wolverhampton goal.