It was Zubar's first goal for the Molineux men since his £2million move from Marseille and it could not have come at a better time.
With Sylvan Ebanks-Blake struggling to regain his goalscoring form of last season, Wolves struggled to make an impact in their bid to make the fifth round for only the second time in the last seven seasons.
Palace produced a battling performance and twice took the lead through Alan Lee and their star performer Darren Ambrose, only to be denied by efforts from David Jones and Zubar.
Wolves, who were taking a welcome break from the rigours of the Premier League, drafted 20 year-old on-loan winger Geoffrey Mujangi Bia from Charleroi into their squad as manager Mick McCarthy made seven changes.
But it was cash-strapped Palace who sprang the early surprise when they took a third-minute lead to shock the Molineux men.
It should not have been such a surprise because the Londoners - unbeaten in their previous five games - have been playing with a great deal of confidence.
This was demonstrated when Ambrose picked out Lee to notch a comparatively easy goal with a close-range header.
Shell-shocked Wolves could have found themselves in even deeper trouble but Ambrose missed a golden opportunity to the frustration of the Palace fans.
They suffered an even more serious setback when central defender Claude Davies was injured after a fall and the game was held up for six minutes.
But Palace continued to pose problems to Wolves, who slowly worked their way back and were on level terms in the 37th minute.
A cross from Kevin Foley was headed on by former the former Southampton player to to Jones, who drilled his shot past Julian Speroni to the relief of McCarthy.
But the Wolves boss was far from happy four minutes into the second period when Scotsman Christophe Berra fouled Lee just outside the area.
Ambrose spotted an opening in Wolves defence and slammed his free-kick past Wayne Hennessey for his 14th goal of the season.
Substitute Kevin Doyle raised Wolves' hopes with a header which hit the bar but with time running out Zubar was on hand to convert a Kevin Foley cross to earn a replay.