Ro-Shaun Williams' own goal was all Liverpool needed to progress to the fifth round of this year's English FA Cup championship.
The 21-year-old full-back mistakenly headed Neco Williams long pass beyond the reach of his goalkeeper Max O'Leary before dropping straight into the net.
Jurgen Klopp's men advanced to the next stage of the competition 3-2 on aggregate having played 2-2 in their initial meeting late last month.
Although the visitors found the back of the net, the Video Assistant Referee chopped off the goal for offside.
It was Nigerian-born forward Daniel Udoh who came in the 57th minute who launched a low cross into the opponent's danger zone which was saved by Caoimhin Kelleher.
But was on ground to head into the net a rebound which the VAR eventually ruled out for offside.
It was moments later in the game that William's own goal cost the Shrews a chance to reach the next stage of the competition.
The German-born boss once again refused to field any of his first-team players for the game as he focuses to win the Premier League in grand style.
Klopp's men currently sit atop of the EPL table with massive 73 points from 25 league matches - 22 points ahead of defending champions Manchester City.
Liverpool vs Shrewsbury Town: Williams' own goal hands Reds 1-0 win
They are also seven matches away from matching Arsenal's 49-match unbeaten run over 15 years ago.
Klopp started the trio of Liam Millar, Harvey Elliot and Curtis James up front, with Caoimhin Kelleher in the middle of the sticks for the Merseyside team.
The former Borussia Dortmund man also gave academy coach Sam Ricketts the chance to sit at the stands and watch his lads bring glory to the Reds in the replay.
Liverpool have now been paired with Chelsea for the fifth round of the competition as they edge closer to winning treble this season.
They are in line to win their first Premier League title this season, while their Champions League title defence continues as they battle Atletico Madrid later this month.