Two penalty shoot out saves from Owain Fon Williams earned Tranmere a place in the third round of the Capital One Cup.
Cole Stockton's first half strike put Rovers ahead only for Jermaine Beckford to level after half time.
The sides then couldn't be separated in an entertaining game at Prenton Park throughout extra time before Rovers netted all four of their spot kicks and Fon Williams produced the saves to see his team through.
Ronnie Moore made five changes to his injury-hit side with Ian Goodison, Jason Koumas, James Rowe, Cole Stockton and Danny Holmes all starting in place of Stephen Foster, Abdulai Baggie, Andy Robinson, Ryan Lowe and the suspended Andrai Jones.
Jean-Louis Akpa Akpro headed over a corner from Koumas in the sixth minute, while Rob Hall sent a long range shot wide of the target at the opposite end moments later.
Ian Goodison ended an attack from Hall on eight minutes and Taylor did well to head clear a cross from Oluwasanmi Odelusi soon after.
Tom Eaves' first time volley hit Goodison in the face on 20 minutes and Hall dragged a shot wide of the target three minutes later after Rovers had only cleared a corner as far as the edge of the area.
On 32 minutes Rowe brilliantly weaved his way past two men on the left touchline before his cross for Akpa Akpro was turned behind for a corner and Stockton headed a Power cross on to the roof of the net as Rovers stayed in the Bolton half.
With the game looking set to go into half time goalless, Cole Stockton opened the scoring in added time. The ball fell to the striker on the edge of the area and he controlled before curling a shot past Lonergan into the top right corner.
Akpa Akpro volleyed across goal and wide three minutes into the second half when a Bolton clearance hit Holmes and deflected into his path inside the area.
Goodison blocked a 25 yard shot from Mohamed Kamara on 51 minutes and Rovers survived a goalmouth scramble seven minutes later. After an Atkinson shot had been charged down, Bolton quickly broke forward and won a free kick on the edge of the Tranmere area following a foul by Koumas. Though the initial set piece was cleared, it was the corner that followed that gave Bolton their chances. Taylor and Goodison blocked shots before Fon Williams saved from Alex Baptiste and then got up quickly to superbly palm away Eaves' follow up.
The visitors drew level on 65 minutes. A throw in from the left was played to Baptiste and his through ball released substitute Jermaine Beckford into the Tranmere area and he slid a low shot past Fon Williams and into the right side of the goal.
A 25 yard drive from Eaves deflected off Goodison for a Bolton corner on 72 minutes and the Bolton striker fired wide from wide on the right side of the Rovers area five minutes later.
The Championship side kept pressing. Goodison threw his body in the way of a long range Baptiste shot on 78 minutes and Beckford volleyed over from 20 yards.
Rovers remained a threat on the counter attack but two Stockton crosses were cut out by the visiting defence.
At the other end Eaves looked like he had scored Bolton's second when he lobbed Fon Williams under pressure from Goodison on 84 minutes but Horwood cleared off the line with an overhead kick.
A minute later Beckford bundled Akpa Akpro off the ball but play continued and Bolton soon had the ball back in the Tranmere net, however Eaves' tap in from a Hall cross was ruled out for offside.
A cross from Stockton was just too fast for Rowe to reach in the first minute of injury time while Power shot wide from 20 yards seconds later.
The last chance of the 90 minutes for Rovers fell to Goodison from a free kick but he was quickly surrounded by Bolton defenders and the visitors cleared.
The action went from end to end in extra time. Power wasn't too far away with a curling shot from 30 yards three minutes into extra time while Fon Williams did well to keep out a Beckford shot soon after.
Atkinson played a one two with Stockton before seeing his 20 yard shot blocked by the Bolton defence on 98 minutes and Taylor threw his body in the way of another attempt from Beckford on 102 minutes.
Goodison, still on his feet and putting in a remarkable performance for a 40-year old, pulled off a great interception to deny Beckford a clean run on goal on 107 minutes.
Akpa Akpro fired over on 107 minutes and Atkinson missed the target with a long range effort soon after.
Eaves had another goal ruled out for offside when he fired in at the near post from Baptiste's pass on 110 minutes and Goodison produced a fine tackle to dispossess Andre Moritz as he ran towards goal on 118 minutes, the final chance of the game.
Moritz 1-0 Saved
Akpa Akpro 2-0
Baptiste 4-2 Saved
Tranmere: Fon Williams, Holmes, Taylor, Goodison, Horwood, Power, Koumas (Kirby 74), Atkinson (Baggie 112), Rowe, Stockton, Akpa Akpro. Unused substitutes: Mooney, Maher.
Bolton: Lonergan, Mears, Mills, Hall (Youngs 96), Baptiste, Pratley, Vela (Beckford 59), Knight, Eaves, Odelusi (Moritz 64), Kamara. Unused substitutes: Bogdan, Bolger, Spearing.
Referee: Stephen Martin
Yellow cards: None