Nuno Espirito Santo's side have had plenty of success against the Premier League's elite this season and added to their record with a cup victory
Sunday saw a raft of big-price winners in the FA Cup third round.
Monday's solitary clash saw another underdog come out on top, albeit Wolves were given a much better chance against Liverpool than some of the weekend's bigger priced outsiders.
The Reds remain Premier League favourites at 4/5 (1.80) and 9/1 (10.0) to win the Champions League after finishing as runners up last season.
Those who believe the back-to-back losses in league and cup over the last week don’t bode well for their trophy prospects can get Evens (2.0) with 888Sport on the Merseyside club finishing without any silverware this term.
Nuno Espirito Santo's side began the day as 11/4 (3.75) shots to qualify from the tie and around 29/10 (3.90) to beat the Reds in normal time at Molineux.
There was some support for the home side in the hours approaching kick-off though and especially once the team sheets were announced.
Klopp rotated some of his bigger names, although it was far from a B team from the Premier League leaders and they were still 5/4 (2.25) favourites as the action got underway.
Dejan Lovren's early injury did little to help the Reds' cause but a team containing the likes of James Milner, Fabinho, Naby Keita and Xherdan Shaqiri failed the live up to their skinny quotes from the bookmakers.
Goals from Raul Jiminez and Ruben Neves either side of half time saw the home side through to the next round where they will visit either Shrewsbury or Stoke. They’re now 14/1 (15.0) to lift the trophy this season with 888Sport.
Wolves had already achieved some notable results against the 'Big Six' since their return to the top flight.
Having held Manchester City to a draw at home, the West Midlands club have since gone on to beat Tottenham and Chelsea, plus taken a point from trips to Arsenal and Manchester United.
With that in mind, when Santo named what was a full-strength line-up for this cup clash, it was understandable to see punters getting behind the hosts and they duly delivered.
Liverpool will be looking to bounce back as they head to Brighton this weekend. 888Sport go just 3/10 (1.30) that Klopp’s side get back to winning ways at the Amex Stadium.