Divock Origi started as Liverpool's main striker with Roberto Firmino consigned to the substitutes' bench due to an ankle injury sustained against Manchester United. But the Belgian was largely anonymous in a frenetic first period, with Mohamed Salah instead having the side's best chances.
The Egyptian's best chance to open the scoring came on 28 minutes, when, having been released by a superb Jordan Henderson long ball, he found himself one-on-one with Everton goalkeeper Jordan Pickford. But his shot was telegraphed, and Pickford dived to his right to save.
Theo Walcott had an opportunity shortly before the break, making a rare escape from Andy Robertson down the right before slamming his shot over the bar.
The second half brought a flurry of chances, beginning with Dominic Calvert-Lewin forcing a good save from Alisson from a corner. Liverpool immediately broke down the other end of the pitch and earned a free-kick, but Trent Alexander-Arnold's effort didn't trouble Pickford. Two Liverpool chances in successive minutes followed almost immediately after, with Divock Origi making his only contribution of the match by swinging a shot wide from just outside the area.
Moments later Salah was put through on goal again, but just as he shaped to dink the ball over the onrushing goalkeeper, Michael Keane flew out of nowhere with a superb sliding tackle to dispossess the Liverpool forward.
Liverpool had gone through the gears, and came close again 20 minutes from time when Virgil Van Dijk knocked a header down for Fabinho. The Brazilian midfielder made a crucial error in trying to control the ball before shooting, and his heavy touch was pounced upon by the Everton defence. By this point Firmino had been sent on in desperation, but the Brazilian struggled to impact the game during the short time he was on the pitch.
As the clock ticked towards 90 minutes, Everton had managed to stall Liverpool's momentum and largely held their rivals at arm's length, with Jurgen Klopp growing increasingly exasparated as he watched his side send pass after pass wayward. The goalless draw will suit the blue half of Merseyside a lot better than the red, with this result meaning the title is now in Manchester City's hands.