Record signing Kevin Doyle was denied a late winner which would have capped an impressive full Premier League debut for Wolves as they drew 1-1 with Hull at Molineux.
The £6.5million capture from Reading saw his close-range shot somehow blocked on the line by Tigers captain Michael Turner. Geovanni had given Hull a third-minute lead but Wolves grabbed a deserved point through defender Richard Stearman early in the second half and had the chances to claim victory.
Phil Brown's side, fresh from their first home league win of 2009 against Bolton last week, were relatively untroubled during the opening 45 minutes with Boaz Myhill seldom tested.
But there was more purpose and creativity about Wolves' play as they dominated the second half. Doyle linked up well with Andy Keogh while Matt Jarvis was full of industry and running on the left side of midfield.
It was Jarvis who had the first attempt on goal inside the first two minutes, turning inside the Hull box and firing a low drive straight at Myhill. But the Tigers stunned the home fans by taking the lead via their first meaningful attack through Geovanni 60 seconds later.
Stephen Hunt was the creator with some trickery on the left before he cut into the Wolves area and past the challenge of Greg Halford. His centre picked out the unmarked Geovanni, who had the simplest of tasks to head home from close range.
Hull defender Steven Mouyokolo became the first player to be booked in the eighth minute after a challenge on Doyle and then kicking the ball away.
Doyle was soon causing problems and, from one free-kick he earned, Keogh flashed a header wide from Milijas' ball into the box.
But Hull threatened on the counter-attack and Kamel Ghilas found himself in plenty of space at the far post to meet a Hunt header but directed it straight at Wayne Hennessey.
Myhill made his first meaningful save after 26 minutes when he held a rising shot on the turn from Keogh, who turned sharply after Jarvis had threaded the ball across the box.
Geovanni was spoken to by referee Stuart Attwell after a late tackle on Milijas, although he did not actually make contact with the Wolves midfielder. Keogh managed to get in a shot inside the box but a deflection off Turner took the sting out of the ball and the same player dragged a shot well wide of Myhill's right hand post.
The second half started in dramatic fashion with Wolves' England Under-21 defender Stearman equalising after only 44 seconds.
Michael Mancienne floated a free-kick from inside the centre circle into the Hull area, Craddock flicked the ball on and Stearman timed his run perfectly to half-volley the ball past Myhill from close range.
It was his second goal for the club since moving from Leicester on a four-year deal last summer. Wolves now enjoyed a spell of concerted pressure and Myhill went down to cling on to a Jody Craddock header after Jarvis had seized onto a long throw from Halford and curled the ball back into the danger area.
Elokobi then had time and space to run down the left flank and his centre picked out Keogh, whose firm header was saved by Myhill. Keogh squandered a golden chance with 15 minutes remaining when he was put clear by Elokobi but scuffed his shot wide of the far post.
Then Doyle was denied the winner when Turner blocked his fierce shot on the line. Defender Andy Dawson was booked for time-wasting when taking a throw as Hull tried to wind down the clock. There was encouragement for both sides though.