A half-time telling off from Tranmere boss Micky Mellon helped inspire his side to a 12-11 penalty shoot-out win after they came from 2-0 behind to draw 2-2 with Accrington in normal time.
A staggering 26 penalties were taken with Rovers keeper Mateusz Hewelt saving from Joe Pritchard while his counterpart Lukas Jensen kept out Rhys Hughes before it went to sudden death.
Then Hewelt superbly denied Shaun Whalley as the players stood up to take them for the second time to send League Two Tranmere into the second round.
Two quick-fire goals gave Stanley a 2-0 lead. In the 37th minute Korede Adedoyin fired into the far corner of the net before Ryan Astley's shot went in off the post three minutes later.
Rovers got one back in the 62nd minute through Josh Hawkes and, with almost the final kick of the game, Paul Lewis slid in at the far post to take the game to penalties, with Astley getting the last touch.
“We need to be at it from the off,” said Mellon. “The players shouldn't need abuse at half-time to kick-start them. We should never be outfought and we were too lame in the first half.
“In the second half we showed more of those qualities but there are still areas to improve.
“To be 2-0 down and turn it around to 2-2 and win on penalties is credit to the lads.
“We brought Mateusz from non-league as a number three but he is way ahead of that and he showed it.”
Stanley boss John Coleman said: “They must have thought they were dead and buried at half-time and we should have been more than two goals ahead. Then we meandered through the second half and gifted them two goals.
“Penalties are a lottery – there were some unbelievable penalties – but we are disappointed.
“Tranmere seem to have the hex over us. Whatever we do, we can't beat them.”
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