Claudio Bravo was the hero as stuttering Manchester City needed penalties to see off hard-working Wolves and make the Carabao Cup quarter-finals.
Pep Guardiola's Premier League leaders hosted Nuno Espirito Santo's Sky Bet Championship table-toppers in a match that promised much but failed to deliver goals over 120 minutes.
Often-maligned Bravo saved City's blushes on several occasions during the match and proved the spot-kick hero, denying Alfred N'Diaye and Conor Coady as the hosts won the penalty shootout 4-1 after the game ended 0-0.
Displaced between the sticks by summer signing Ederson Moraes, this was just the Chilean's third appearance of the season and came as both sides made nine changes apiece.
Bravo produced several fine stops to deny Wolves when they ventured forwards, while Sergio Aguero tried and failed to become City's all-time top scorer.
The Argentina international did manage to find the net and secure progress with a cheeky Panenka at the end of a shootout, but it was the saves of N'Diaye and Coady's efforts that were key.
Few could have foreseen the match going so long given the way Aguero started it.
Wolves goalkeeper Will Norris denied him early on, then saw the City striker badly drag wide and volley over.
The tempo soon slowed as Wolves sat deep in a bid to stay resolute and spring counter-attacks.
Raheem Sterling prodded wide as set pieces offered the visitors another route to goal, with Ryan Bennett's header from a free-kick forcing Bravo into action.
Aguero was proving a nuisance at the other end and Yaya Toure wasted a free-kick, only for Wolves to threaten a shock first-half opener.
Bright Enobakhare all too easily shrugged off Eliaquim Mangala and went straight for the City goal, only to be denied one-on-one by Bravo.
Rain fell as Aguero flashed across the face of goal at the start of the second half as the hosts continued to be frustrated.
City's intricate build-up was not creating clear-cut chances - something that should have been punished when Helder Costa was slipped through, only for Bravo to stand his ground and pat away.
Norris atoned for a hashed clearance straight at Aguero and Enobakhare wasted another glorious chance, getting away with a barge on Mangala only to dawdle in front of goal.
City dominated the remainder of regulation time as Sterling directed wide, while Aguero had penalty appeals rejected and Danny Batth denied Ilkay Gundogan at the end of a marauding run.
City's pressure left gaps that Enobakhare threatened to expose at the death.
Racing from inside his own half, the 19-year-old had two players breathing down his neck by the time he shot straight at Bravo under pressure.
The result was extra-time followed and the desperation for victory was epitomised by Toure taking a tumble before Coady made contact, leading to a booking for simulation.
Substitute Kevin De Bruyne and Sterling were leading the City charge as they looked to finally breach the Wolves goal - something that would not come to pass in the opening period of extra-time.
Sterling, Leroy Sane and Aguero all had efforts, while Wolves Ruben Vinagre had hearts in mouths before the end of extra time.
Now using the ABBA system, the first three penalties were scored before N'Diaye slipped and saw his attempt saved by Bravo.
The Chilean then denied Coady's spot-kick and Aguero went on to wrap up progress.