Carling Cup Result : Liv 2 - Crewe 1
Jermaine Pennant was a constant menace on the right flank while Lucas and Daniel Agger produced assured performances to give the Spaniard a selection poser for the game against Everton.
Agger gave Liverpool a 15th-minute lead from a free-kick before Michael O'Connor's equaliser 10 minutes later.
Pennant supplied Liverpool's second goal with a dangerous cross which was headed home by Lucas in the 58th minute but really the margin of the victory should have been greater.
While strengthening the Reds first team for a Barclays Premier League title challenge has been Benitez's priority he is attempting to build a squad to challenge on several fronts.
• Rafa satisfied with resultThe manager included only one English player - Pennant - in his starting line-up as he handed debuts to Brazilian goalkeeper Diego Cavalieri and Swiss defender Philipp Degen.
Sami Hyypia, named as captain, and Agger were recalled in central defence while there were places for Lucas, Emiliano Insua and Damien Plessis while Nabil El Zhar, Ryan Babel and David Ngog carried the attacking threat.
Crewe first-team coach Steve Holland included former Liverpool youth team defender Danny O'Donnell alongside captain Julien Baudet at the back.
Degen and Pennant linked up well down the right flank in the eighth minute to create Liverpool's first chance.
Breaking from a Crewe free-kick, Pennant slipped a clever ball to Degen on the overlap and he whipped a low cross into the penalty area but neither Ngog nor Babel were able to get a touch.
Pennant continued to provide the home side's best outlet and Crewe defender Billy Jones was lucky to escape a booking after a late challenge on the winger in the 12th minute.
Liverpool's pressure eventually paid off three minutes later after Ngog was fouled on the edge of the penalty area by O'Connor.
Denmark defender Agger took the resulting free-kick and smashed a powerful low effort past goalkeeper Steve Collis.
Crewe equalised in the 25th minute after Byron Moore's shot was deflected by Agger for a corner.
Jones crossed and Calvin Zola's header was parried by Cavalieri but O'Connor made amends for his earlier foul when he slammed home from close range.
The Railwaymen began to settle but it was Liverpool who created the next opportunity in the 41st minute.
Hyypia was picked out on the penalty spot by a Pennant corner but Collis blocked his shot and Plessis could only fire the loose ball into the crowd.
Babel went close moments after the interval when his shot from the left edge of the penalty area was deflected and wrong-footed Collis but looped on to the roof of the net.
Liverpool restored their lead in the 58th minute after good work down the right flank by the impressive Pennant.
The lively winger delivered a dangerous cross into the penalty area and Brazil midfielder Lucas timed his run superbly to direct a header past Collis.
Benitez surprisingly introduced Fernando Torres and the Spain international was immediately involved.
Pennant delivered another ball into the penalty area in the 82nd minute and Torres' header was tipped past the post by Collis.
The Crewe goalkeeper saved again from the Spaniard two minutes later after Torres had broke clear of the Crewe defence.
Liverpool were given a few late scares as Crewe pressed for an equaliser but held on to secure their place in the next round.
Liverpool manager Rafael Benitez was satisfied with his side's performance after they secured their place in the fourth round of the Carling Cup with a 2-1 win over Crewe.
''It was one of those types of games where if you do not score the third goal and finish the game then it can be difficult,'' he said.
''We were a little bit nervous today and we certainly had enough chances to score a third goal.
''Tonight we can talk about two good goals - Daniel Agger's free-kick was a fantastic strike and also Lucas is a player that likes to get into the box and I am confident he can score more goals like this.
''It was a very positive result and a positive reaction from the players and perhaps the only thing is that we could not score the third goal.''
Benitez explained the decision to introduce Fernando Torres in the second half despite the Merseyside derby at the weekend.
The Spain international had an immediate impact and was twice denied by Crewe goalkeeper Steve Collis.
Benitez added: ''We brought Torres on to try and score the third goal - every competition is important so we were trying to create more chances.
''So going forward Torres would give us more space and you could see he had two chances to score which if they would have gone in would have sealed the game.
''I was thinking the same with Robbie Keane but we had a problem with Philipp Degen so I was not able to put him on earlier to put him in a position to score.''
Crewe first team coach Steve Holland was proud of the way his side acquitted themselves and said a trip to Anfield last week helped settled any pre-match nerves.
''I brought the players to Anfield to do the stadium tour last week so they were not overawed by the whole experience of playing here,'' he said.
''Admittedly there was a mass brawl to get Fernando Torres' shirt afterwards but overall I think they didn't show any signs of nerves on the night.
''We acquitted ourselves well - we stuck to our game plan and could have even have nicked an equaliser at the end with a couple of late chances.''
