The hosts took the lead when Jonathan Walters capitalised on a Sebastian Coates mistake to set up Kenwyne Jones, only for a second-half brace from Suarez to turn the game on its head.
The Uruguayan was in scintillating form. His first was an excellent individual goal in which he nutmegged Stoke youngster Ryan Shotton before curling a strike inside the far post, whilst his second showcased his predatory instincts as he reacted to a looping Henderson cross by getting clear of his man and heading into the far corner.
“His goals were brilliant,” the former Sunderland man told reporters. "The first one was a piece of individual class but that’s what he is, he does it every week.”
Having played 90 minutes on the right of the Reds’ midfield, Henderson was also keen to praise the collective performance.
“It was a good win in the end," he continued. "I thought we started well and carried it through the game and we deserved the win.
"We showed a lot of character [to come back] and were disappointed that we went 1-0 down anyway as we played so well and created chances to go ahead.”
Despite missing a number of chances for the visitors, Andy Carroll was also the subject of praise from Henderson.
“I thought Andy was brilliant tonight, I thought he worked really hard," Henderson added.
"He was closing defenders down, winning headers and he had a few chances himself and I thought he contributed a lot tonight.”
The England under-21 international has played a key role in Liverpool’s advancement to the quarter-finals but Kenny Dalglish's side will have to wait until Saturday’s draw to find out their next opponents in the competition.