Liverpool dominated the game and went ahead late in the first half when Mohamed Salah curled home his 13th Premier League goal of the season.
However, the Reds could not extend their lead and were made to pay late on when Dejan Lovren conceded a penalty that Rooney placed past goalkeeper Simon Mignolet.
Liverpool boss Jurgen Klopp surprised many with his starting lineup, leaving influential duo Roberto Firmino and Philippe Coutinho on the bench and bringing Dominic Solanke into the attack and James Milner into midfield.
Goal's Melissa Reddy shared the teamsheet:
Despite the changes, the hosts dominated the first half, with Everton rarely venturing out of their own half.
ESPN FC's Glenn Price highlighted how the visitors offered little as an attacking force:
However, despite all Liverpool's dominance, they struggled to force goalkeeper Jordan Pickford into action.
Match of the Day's Twitter account gave a neat illustration of the nature of the first half:
With half-time looming, Liverpool were in need of some inspiration, and it duly arrived in the shape of the Premier League's top scorer.
The Egyptian showed strength to shrug off Cuco Martina before wriggling past Idrissa Gueye and bending his shot around Ashley Williams and goalkeeper Pickford to open the scoring in style.
Liverpool writer Ben Webb explained just how good Salah's strike was:
Suddenly Liverpool were rampant, and Alex Oxlade-Chamberlain flashed a shot just wide before Sadio Mane led a swift counter-attack but dragged his effort wide.
Everton made two changes at the break, bringing on Aaron Lennon and Morgan Schneiderlin as manager Sam Allardyce sought a way back into the match.
However, Salah almost doubled the Reds' lead minutes after the restart, heading Milner's cross just wide at the far post.
The Egyptian was giving Martina torrid time at left-back because of his pace and skill on the ball. Tony Scott at the Liverpool Echo summed up the Everton man's performance:
Martina will have been relieved to see Salah replaced just after the hour mark, with Firmino coming on his place. But although Liverpool continued to dominate, they could not extend their lead.
They Reds were then made to pay for their profligacy with 15 minutes to go, when Lovren pushed Dominic Calvert-Lewin in the area to concede a penalty.
Up stepped Rooney, who hit the penalty straight down the middle to level the scores.
ESPN FC's Liam Twomey was critical of Lovren's defending:
Football writer Daniel Harris said the blame lay elsewhere:
Klopp sent on Coutinho and Danny Ings in response, and the Reds piled on the pressure in the closing stages but could not find a way through.
Although Liverpool still picked up a point, they will be hugely disappointed not to have won a game they dominated. But their vulnerable defence once again cost them points.