The second-tier team threatened from a series of set-pieces late in the game but could not find an equalizer against their Premier League opponents who took the lead in the 28th minute through Ivan Cavaleiro.
Cavaleiro, one of three changes to the Wolves line-up, was left in space to fire in Matt Doherty’s cutback with what was the first shot of the game at Ashton Gate.
Bristol goalkeeper Frank Fielding joined the attack during a late corner but had a shot saved by opposite number John Ruddy.
Crystal Palace won 2-0 at third-tier side Doncaster later Sunday, and Swansea trailed 1-0 at halftime before beating Brentford 4-1 in an all-second tier meeting.
Palace took the lead after eight minutes in their first attack. Jeffrey Schlupp drove the ball down from inside his own half and slotted into the far corner after his effort took a deflection off Paul Downing. Max Meyer doubled Palace’s lead moments before halftime as he glanced home Andros Townsend’s header across the six-yard box.
Palace’s progress in the cup has implications for already eliminated Tottenham.
The next possible date for the opening of Tottenham’s delayed new stadium was for a Premier League game against Palace on March 17 but the south London club will now be playing its FA Cup quarterfinal that weekend.
Tottenham’s next scheduled home game after that is April 6 against Brighton. But Brighton could be contesting a cup semifinal that weekend if it wins its quarterfinal.
Tottenham had hoped last year to move into its new 62,000-capacity home on the site of its old White Hart Lane stadium
Brentford went ahead at Swansea just before the half-hour mark after Ollie Watkins fired into the top corner. Swansea sparked a comeback with an equalizer four minutes after the break through a Luke Daniels own-goal following a free kick from Bersant Celina. Dan James, Celina — ending a solo run with a sweet finish into the bottom corner — and George Byers also scored.
Brentford defender Ezri Konsa Ngoyo received a straight red card just after the hour mark following a professional foul on James.
Premier League champion Manchester City, Watford, Brighton and Millwall advanced Saturday.
The fifth round is completed on Monday when holder Chelsea hosts Manchester United.