Marco Silva's substitutions proved inspired as late goals from Dominic Calvert-Lewin and Cenk Tosun helped Everton to a 2-0 win over Crystal Palace, who had a Luka Milivojevic penalty saved.
The match appeared to be heading for stalemate after Jordan Pickford denied Milivojevic from 12 yards on the hour, but Everton scored twice in two minutes with the clock winding down to secure a third successive Premier League win.
Everton created several chances in a first half they generally controlled, but Palace went closest when Cheikhou Kouyate hit the frame of the goal with a header.
Palace then saw Milivojevic denied from the spot and Everton took full advantage, as Calvert-Lewin headed them into an 87th-minute lead before Tosun added a second on the break.
Despite their control of the game, Everton did not test Wayne Hennessey in the Palace goal until the 28th minute when Gylfi Sigurdsson met Seamus Coleman's cut-back and forced a vital save.
The visitors soon enjoyed a promising spell of their own and went close to the breakthrough – Kouyate heading against the crossbar from close range after James Tomkins nodded Andros Townsend's corner across goal.
Wilfried Zaha won Palace a penalty in the 60th minute when tripped by Coleman, but Milivojevic saw his effort – struck straight down the middle – saved by Pickford's foot.
Theo Walcott wasted a chance soon after, but his replacement – Ademola Lookman – ultimately set up the opener three minutes from time, producing a fine cross for Calvert-Lewin to head home.
Tosun then put the game beyond Palace two minutes later, racing on to Michael Keane's long ball and coolly slotting past the helpless Hennessey, moving Everton up to eighth in the Premier League.
What it means: Silva's subs a masterstroke
With Andre Gomes, Bernard and Walcott not making much of an impact in the second half, Silva withdrew them all. Tosun, Lookman and Calvert-Lewin entered and all three made a vital contribution. The coach could not have hoped for a better answer from his substitutes.
Jordan pick of the bunch
Aside from his generally authoritative display, Pickford's importance to Everton on Sunday was huge. Although Calvert-Lewin and Tosun ultimately took the plaudits with their late goals, had he not saved Milivojevic's penalty, there is every chance Everton would have been too deflated to go on and score.
Walcott wasteful and ineffective
An otherwise quiet day for former Arsenal man Walcott could have been really livened up when he was present with a great opportunity in the second half, but he shot straight at Hennessey. It summed up his day.
Everton face a trip to Old Trafford to face Manchester United next Sunday, while Palace host Arsenal a few hours earlier.
|Wozniacki cruises through in Melbourne|
|Federer maintains perfect Australian Open second-round record|
|Warriors set NBA record, Butler´s 76ers rout Timberwolves|
|´I like the fact we beat them´ - 76ers´ Butler revels in win over Timberwolves|
|Murray says he´ll ´probably´ have operation|
|Australian Open tribute for Andy Murray surprises brother Jamie|
|Warriors score NBA record 51 points in first quarter against Nuggets|
|Panthers owner Tepper doesn´t rule out Newton missing 2019 because of shoulder injury|
|De Ligt will be world´s best centre-back – Koeman|
|Ronaldo a ´perfect machine´, says Gattuso|
|Barcelona? I can´t say anything - Stuani|
|Silva upbeat about Man City title chances|
|Celtics youngsters say Irving´s callout ´came from a good place´|
|NFL playoffs: Patrick Mahomes v Tom Brady|
|NFL playoffs: Jared Goff v Drew Brees|
|Sixers sign Brewer to 10-day contract|
|Lozano and Morgan scoop CONCACAF awards|
|Lakers ´optimistic´ about LeBron injury|
|Giants produce mammoth fourth quarter against Nymburk|
|Austin FC to join MLS in 2021|
|Henry, Vieira look forward to reunion when Monaco host Nice|
|Barcelona reject Neymar phone call reports|
|Wentz is the quarterback ´going forward´, says Eagles coach Pederson|
|Gattuso: Higuain has not asked to leave|
|Drew Brees by the Opta numbers: 10 facts for QB´s milestone birthday|
|Harry Kane injury: England captain´s history of ankle woe|
|Harry Kane injury: Opta numbers suggest Spurs struggles|
|Harry Kane injury: Tottenham´s options in striker´s absence|
|Allegri: Supercoppa clash practice for Champions League knockouts|
|First in clean sheets, second to Schmeichel in titles – Cech´s Premier League career in Opta numbers|
|Warrington sign England star Widdop|
|Gatland confident Wales can win Six Nations|
|Fulham sign Netherlands international Babel|
|Harry Kane injury: Games the Tottenham striker will miss|
|Simeone focused on matches, not transfer dealings|
|Iran v Iraq: Pressure off for Queiroz & Katanec|
|Vietnam v Yemen: Kocian keeps the faith|
|Darren Bravo back in West Indies Test side for first time since 2016|
|Kane out until March with ankle injury|
|South Korea v China: Son arrives for Group C dead rubber|
|Kyrgyzstan v Philippines: Eriksson remains hopeful|
|McGrath to miss Six Nations, Sexton nearing fitness|
|Kohli savours Dhoni ´classic´|
|Ford: People obsess over Farrell fly-half battle|
|EFL asks Leeds to explain ´spygate´ scandal|
|No alarms for Djokovic and Zverev, Raonic masters Kyrgios|
|Australia 3 Syria 2: Rogic breaks hearts with stoppage-time winner|
|Palestine 0 Jordan 0: Socceroos winner keeps hopes alive for Lions of Canaan|
|Halep: The results don´t matter any more|
|Hard work for Halep as Serena and Osaka sail through|
|Napoli director to take legal action over ´false´ quotes about Rog move|
|Alexander-Arnold facing absence of up to four weeks|
|Solari: We only have one number nine at Real Madrid|
|Halfpenny & Young named in Wales´ Six Nations squad|
|Crawford v Khan confirmed for April 20|
|Centurion Kohli inspires India to level ODI series|
|Wagner hails Huddersfield togetherness after exit|
|Hughes to join Bristol, Le Roux also leaving Wasps|
|ICC appoints Sawhney as new CEO|
|Forest appoint club legend O´Neill as new manager|
|Halep digs deep to gain revenge over Kanepi|
|Cech to retire at the end of the season|
|Brisbane Roar 0 Melbourne Victory 5: Barbarouses treble sinks Roar|
|´Struggling´ Azarenka breaks down in tears following Australian Open exit|
|Dominant Djokovic coasts through in Melbourne|
|Allardyce admits Huddersfield appointment is ´highly unlikley´|
|Choupo-Mouting: Manchester United have changed|
|Faletau set to miss Six Nations with another broken arm|
|UEFA opens disciplinary proceedings into Chelsea chants|
|Serena´s the greatest ever - Bouchard relishing second-round clash|