And while that lead lasted only a few minutes - Mohamed Salah making it 1-1 at half-time - the Clarets defended superbly to stop Liverpool breaking through again before nearly pinching a famous win themselves through inspirational stand-in skipper Ben Mee in a breathless finish.
The 2017-18 Premier League season kicked off with a disappointing Liverpool result, as they conceded an 96th minute goal in a 3-3 draw at Watford.
However, with Nick Pope in fine form between the posts for the Clarets, Liverpool struggled to turn their dominance into goals.
"I didn't want to change him at the end, that's why it looked a bit confused as we brought the subs on".
Coutinho makes his first starting lineup of the season.
Burnley sits above Liverpool in seventh thanks to a superior goal difference, having negotiated what looked like an extremely tough start to the season.
Liverpool pushed for the victor but, for all of Coutinho's brilliance, they lacked the cutting edge in the absence of the suspended Sadio Mane.
The Senegalese forward is beginning a three-match ban after being sent off against Manchester City last Saturday, ruling him out of this weekend's match as well as the upcoming league and Carabao Cup games against Leicester City. Liverpool were held to another frustrating draw as Burnley grafted for a well-earned point at Anfield on Saturday.
GK Simon Mignolet, 6 - Made an important save late on to deny Mee and generally dealt with the aerial stuff confidently throughout.
"I was lucky to manage Barcelona with many outstanding performances but this week has been a lot of goals". Errors at one end of the pitch and lack of ruthlessness at the other leaves them winless in their last three fixtures across all competitions.
"More options, that's all good".
It was exciting stuff at Anfield as both teams went for the victor and substitute Dominic Solanke's effort disappointingly hit the crossbar. You don't expect to come to Anfield and out-pass them, and we never planned for that, so the game plan isn't about keeping the ball.