Then substitute Solanke somehow missed from six yards out as his volley cannoned off the bar.
Mohamed Salah has netted five times in all competitions for Liverpool since joining from Roma in the summer.
Coutinho returned for Liverpool on Wednesday in their 2-2 draw with Sevilla in the Champions League.
Player Ratings: Philippe Coutinho of Liverpool attempts to get past Jack Cork of Burnley during the Premier League match between Liverpool and Burnley at Anfield on September 16, 2017 in Liverpool, England.
And it was required after Burnley scored with their only shot of the first half.
30' - GOAL! Liverpool 1-1 Burnley: An immediate equaliser from the Reds as Salah scores a fine individual effort! At some point, somebody like Arsenal will be on the end of another Liverpool hiding but today Burnley got another great result to add to those they got against Spurs and Chelsea in what is shaping up to be a good season for them.
Burnley's surprise point came despite having to field a rookie goalkeeper following the recent injury to Tom Heaton who will be out for several months with a dislocated shoulder. I think you see that when you play on the pitch. Our shape was good and Popey was excellent in goal.
"We have to be strong, I know that, but we really can be strong". You need to have luck in football, and you need to have the referee who makes the right decisions.
With a rotation of seven changes to the starting 11, Jurgen Klopp provided a number of players opportunities to prove their value.
"I was lucky to manage Barcelona with many outstanding performances but this week has been a lot of goals".
"When you have shots on goal it's not about their defending".
"It was really nice how the crowd welcomed him - no one was 100 percent sure about this but the Liverpool family was sensitive enough to do this and for him it was good".
"It's the best we have played against Burnley since I have been in".
Burnley manager Sean Dyche makes no apologies for his side's game plan after coming away with a 1-1 draw against Liverpool at Anfield.
"We draw at Watford, and we drew today after what I saw as a clear penalty situation".