Both sides started the game in typically frenetic fashion but it was the visitors who made the better of the first half chances as last-minute addition Jordon Ibe rattled the frame of the goal before Philippe Coutinho and Raheem Sterling called Joel Robles into a string of saves.
Romelu Lukaku and Steven Naismith combined well in and around the Liverpool area but struggled to create a clear sight of goal in the first half.
Gerrard almost snatched the points with an acrobatic effort but found Naismith in his way.
Brendan Rodgers’ side pushed for the opener in the second half as Daniel Sturridge was introduced, but Robles, and some resolute defending from both sides, ensured the game would end goalless.
Ross Barkley’s inclusion late on opened the game up for both sides and he set up Seamus Coleman at the death to win it for the Toffees but Simon Mignolet produced a fine save as both sides had to settle for a share of the spoils.
Liverpool remain seventh after the draw, four points adrift of the top four while Everton moved a point closer to the top half of the table, they remain 12th.
A raucous atmosphere at Goodison was met by a tense and tactical opening, as both sides jostled for supremacy.
Raheem Sterling was lively from the off and looked to exert his pace early on. However, having collected Philippe Coutinho???s through ball and drawn Joel Robles off his line, should have done more than hit the side-netting after eight minutes. Gerrard called the Toffees keeper into action minutes later as his free kick was tipped out for a corner.
Lucas Leiva went off injured on the quarter-hour mark but Liverpool were unfazed as Robles was called into action again, this time denying Jordon Ibe from a yard as he tried to tap home Sterling???s deflected effort.
Everton responded midway through the half and could have broken the deadlock had Steven Naismith read the flight of Seamus Coleman???s cross and got an effort away.
The best opportunity of the half was created by the 19-year-old Ibe who, after collecting the ball inside the Everton half and running towards goal, unleashed a thunderous drive which rattled the frame of the goal.
Everton rallied but couldn???t get a clear sight of the Liverpool gaol and it was Robles who was called into action again as Coutinho looked to replicate his FA Cup goal against Bolton, but the keeper was pulled off another save.
Daniel Sturridge was brought on five minutes after the break but Liverpool had a string of chances before he entered the fray.
After Gareth Barry???s error, Coutinho rushed his pass and failed to find one of the four team-mates he had in support. He made no mistake in finding a team-mate moments later as he threaded the ball into Sterling, but his shot drew another save from Robles.
And from the resulting corner Gerrard almost broke the deadlock in style with an acrobatic volley which was deflected wide of Naismith.
Ibe continued to run Everton full-back Bryan Oviedo ragged down the right and Sturridge almost benefitted from his efforts, but the substitutes attempt was blocked in the goal mouth.
Things came to a head ten minutes from time as Muhamed Besic???s challenge on Ibe sparked an altercation which lead to Jordan Henderson and Naismith being booked, along with the Bosnia international for his initial challenge.
Barkley???s inclusion opened up the game in a frenetic final few minutes but neither fellow substitute Rickie Lambert, Coleman nor Gerrard couldn???t capitalise on the nature of the game to give their sides the advantage.