The Championship team, who fielded the veteran strike pairing of Eidur Gudjohnsen and ex-Liverpool man Emile Heskey, proved tireless opponents and made it a frustrating evening for their hosts.
Javier Manquillo passed up the clearest opening for Liverpool, while a lively Raheem Sterling was regularly thwarted by last-ditch challenges from a disciplined Bolton defence - behind which goalkeeper Adam Bogdan excelled.
Bolton made a confident start, with Matt Mills seeing an 11th-minute strike blocked before the defender returned to his own penalty area to deny Adam Lallana - making a first Liverpool start since New Year’s Day - with a perfectly timed challenge.
In the 33rd minute, Dean Moxey was inches away from putting the Championship team ahead - his half-volley from the edge of the penalty area whistling narrowly past Simon Mignolet's right-hand upright.
Glen Johnson and Lallana then fired rasping strikes into Bogdan's arms as Liverpool began to find their rhythm during the closing stages of the first half.
Bogdan was out bravely to save at Sterling's feet when Philippe Coutinho unpicked the Bolton defence with a 53rd-minute throughball and the goalkeeper made another fine stop by getting down to push a Coutinho drive away from the bottom corner.
Youngster Conor Wilkinson was introduced in place of Heskey but Gudjohnsen remained and spurned a pair of chances in quick succession.
The former Chelsea and Barcelona man side-footed wide from Ream's low cross before more wastefully blazing over on the end of Wilkinson’s 64th-minute cutback.
Borini headed agonisingly wide in stoppage time and Lucas Leiva saw Bogdan beat away a fierce drive as Neil Lennon's team claimed the replay they craved.
