Brendan Rodgers' men ran out 4-2 winners over Chris Kiwomya' men after a tense final period at Anfield.
Liverpool started as they meant to go on as England starlet Raheem Sterling fired the Reds 1-0 up after just 4 minutes.
Liverpool were dominant throughout, bossing the midfield and when a finely measured Steven Gerrard pass landed at Daniel Sturridge' left boot their was only one place the ball was going to end up, 2-0.
Despite Liverpool' dominance the Notts County lads battled hard and were often dangerous on the counter attack, causing Liverpool' back-line some real problems at times.
And when Emmanuele Smith' flick towards goal met Yoann Arquin' head, County were right back in it, from then onwards Kiwomya' men started to gain confidence and were stroking the ball about accurately, the second goal was imminent.
And when Glen Johnson was caught far too forward, Arquin' square ball found ex-Chelsea winger Coombes, and he made no mistake in levelling his side.
Liverpool had already suffered injury problems within the 90 mins, losing Joe Allen and new boy Aly Cissokho so when Kolo Toure hit the deck with a suspected groin strain, Rodgers had to readjust seeing his side go down to 10 men after using all his substitutions.
But, as Rodgers claimed in the post match interview, his side showed great character and belief, pulling the result firmly back into their hands with two late goals from Daniel Sturridge and Jordan Henderson.
Despite the heartache of losing two extra time goals, Chris Kiwomya' men will use this performance as a platform to build from, after failing to win in any of their five opening domestic fixtures.
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