The Reds dominated the majority of proceedings and wasted a few chances throughout the game before eventually finding the back of the net.
Newcastle went down to 10 men in the later stages of the second half, but the home team was still unable to capitalize.
There can't be too many complaints with individual performances though, and it seems that it's just a matter of time before Liverpool really begin to get the three points on a regular basis.
Here are the player ratings for Liverpool.
Bradley Jones couldn't have done much against Yohan Cabaye's impressive opener, but had a solid game otherwise.
He made a few decent stops in the second half to keep his team's momentum and keep them in the game.
He probably could be criticized for not closing Cabaye down quickly enough, but he and the whole defense were in the process of shifting.
Wisdom provided some attacking threat early on but for the most part gave Liverpool a very solid presence on the right side of defense.
Martin Skrtel didn't have much to do defensively but did it all well. He kept both Demba Ba and Papiss Cisse quiet throughout the game, which is no easy task.
He wasn't loose in possession defensively and helped his team start attacks from the back well.
Daniel Agger was rock solid in defense and worked with Martin Skrtel to neutralize Newcastle's main attacking threats.
Agger made a few forays forward but was always in the right place defensively and as a result hsi team did not let in another goal.
Jose Enrique was beaten a little to easily for the goal but did an okay job on the defensive side.
His willingness to go forward ensured that Liverpool's main attacking threat came from the left side, and he provided the assist for Luis Suarez in the end.
Joe Allen was cool and calm throughout the match and tidy in possession. The fact that he is still the most accustomed to Brendan Rodger' preferred style of play is evident.
He kept Liverpool's attacks moving in the right direction and was aware defensively for the most part.
Steven Gerrard provided some good deliveries from set-pieces and in open play. He was unlucky to have a few long-range efforts blocked outside the area.
He tried to drive his team forward with some his usual quick, long passes forward with without being wasteful in possession and did just that.
Nuri Sahin had some good moments here and there but wasn't too influential. He was tidy in possession and aware defensively. Subbed off eventually for Downing but had an okay outing.
Suso was in and out of the game with both good and bad moments. One notable moment was a mazy run that resulted in a blocked shot and a Liverpool corner.
He didn't make too much of a impact on either end of the pitch.
It looked liked it would be another frustrating afternoon for Liverpool's Uruguayan star as he worked tirelessly to create and finish chances.
He got his reward in the end with a brilliant effort after being sent through by Jose Enrique and showed why he will always be Liverpool's main attacking threat..
Raheem Sterling put in another good shift for Liverpool and was dangerous taking on players and putting in crosses.
Next to Luis Suarez, Sterling was Liverpool's major attacking threat and may not have been close to scoring a goal but Newcastle was wary of him.
Jonjo Shelvey - 6
Jonjo Shelvey missed a few chances when he came on that could have won it for his side. He showed some energy in his minutes on the pitch however but couldn't make the necessary impact as the game was moving at a fast pace.
Stewart Downing - 6
Stewart Downing is still yet to silence critics and probably should have done more in his 10 to 15 minutes on the pitch. He provided a few crosses for teammates but didn't really change the game