Everton are out of the FA Cup after a goal from midfielder Curtis Jones with 19 minutes remaining settled this all-Merseyside third round tie.
Carlo Ancelotti’s side created the lion’s share of opportunities and three times in the opening half were denied by good saves from home goalkeeper Adrian.
The visitors hadn’t been especially disturbed by Liverpool when Jones took possession 18 yards out and cracked home a shot off the underside of the bar.
Manager Ancelotti, who had already brought on Moise Kean and Fabian Delph, made his final throw of the dice with the introduction of Bernard. But despite a late chance for Kean, who hooked over from a Djibril Sidibe cross, the home team held out.
Adrian was twice forced into reflex saves as the contest bubbled from the off.
Gylfi Sigurdsson drifted a ball to connect with Theo Walcott’s perfectly-timed run behind Liverpool’s defence on six minutes, Walcott held up by James Milner, who injured himself in the process.
Dominic Calvert-Lewin rushed onto the loose ball and powered it goalwards only to be denied by Adrian’s legs.
Calvert-Lewin and Walcott would come close to linking to telling effect later in the half when the former flung himself at the latter’s centre but was inches from connecting.
Back to Adrian, whose second major stop came after 12 minutes. Calvert-Lewin’s strength and speed were bothering Liverpool’s central defenders and Nathaniel Phillips’s determination to avoid being turned led him to flatten the forward from behind.
Sigurdsson’s free-kick found Mason Holgate peeling off the back of Jones and heading an effort Adrian beat away from underneath his bar.
Phillips won admirers among the home crowd for a full-blooded challenge on Richarlison but subsequently blotted his copybook with a loose pass seven minutes before half-time.
Morgan Schneiderlin was the recipient and he fed Sigurdsson, who passed forward to Walcott. The Englishman laid off to Calvert-Lewin but the striker’s shot from 20 yards flashed wide.
Adrian’s third significant contribution of the opening half arrived on 27 minutes.
Sidibe – operating in advance of Seamus Coleman – rolled a ball down the line for Walcott.
Richarlison arrived to meet the cross with a first-time strike from 10 yards that Adrian repelled with his right boot.
Adrian’s counterpart Pickford, meanwhile, had a quiet time of it until four minutes before the break.
Adam Lallana, twice, had been off target with efforts from distance, and Takumi Minimino was wide with a header from close in – but it wasn’t until Divock Origi manipulated his own shooting opportunity that Pickford was tested.
The Everton goalkeeper was equal to Origi’s low drive, diving right to fingertip the ball round the post.
Jones cut in from the left and hit beyond the far post, while Holgate intervened when Lallana tried to dash into the box.
Coleman was in the thick of it for Everton, the Irishman’s tackle on Jones every bit as meaty as the one Richarlison received from Phillips.
The Everton skipper twice defended well at the back post from deep crosses, too, Coleman taking to his new centre-half-cum-right-back position very nicely indeed.
Everton finished the first half trying to put the squeeze on their hosts. Richarlison ran into traffic following Walcott’s lobbed pass and when the ball was recycled into the area by Sidibe the Brazilian saw it too late to steer his header on target.
Schneiderlin fizzed an effort over after a corner was partially cleared soon after the restart and Pickford was tested after a fashion by right-back Neco Williams’s 25-yard blast.
Coleman was too strong for Lallana on 55 minutes, brushing aside the midfielder and finding Walcott. He found Sidibe, who transferred the ball to Richarlison, as Everton injected pace and purpose into their counter.
When Richarlison hesitated, though, it was fatal and the South American was swallowed up by a scrum of red shirts.
Pickford saved an awkward, bouncing Origi strike from range with 21 minutes remaining before Jones took aim to leave the keeper helpless two minutes later.
Substitute Alex Oxlade-Chamberlain was thwarted by Pickford at the foot of his right post before Schneiderlin struck too high after another corner eventually reached him 18 yards from goal.
Kean was wide of the far post from Sidibe’s stoppage-time delivery and Everton were left to rue passing up a handful of first-half opportunities.