Everton striker Dominic Calvert-Lewin was controversially sent off but the 10-man Toffees held on to force an FA Cup third-round replay with Crystal Palace.
Calvert-Lewin was shown a straight red card in the 79th minute after on-field referee Chris Kavanagh had been advised to review the incident on a pitchside monitor after an intervention from Video Assistant Referee Michael Salisbury.
The England forward had his studs up as he slid in to win the ball in a challenge on Nathaniel Clyne and clipped the defender’s shin, although contact was minimal.
Everton fans booed the decision when the incident was replayed on a big screen at Selhurst Park, with Toffees boss Sean Dyche also shaking his head, unhappy at the verdict.
Calvert-Lewin, now without a goal in 12 matches, had earlier had one of the few clear-cut chances but could only shoot tamely at home goalkeeper Dean Henderson.
Jefferson Lerma fired just over from 20 yards for the Eagles, but Palace could not make their extra-man advantage count.
Everton also suffered what looked to be a serious injury to winger Dwight McNeil, who was carried off on a stretcher with a leg injury late on.
Draw a fair result, as the two sides have to do it again
Eberechi Eze nearly won it for the hosts in the eighth minute of nine added on at the end, but Everton goalkeeper Joao Virginia did well to push the strike around the post.
Palace had gained a 3-1 Premier League win over Brentford on December 30 to end an eight-game run without a victory, but were without the injured Michael Olise, who hurt his hamstring after scoring twice in that match.
Striker Jordan Ayew was also unavailable, as he was with the Ghana squad before the Africa Cup of Nations, which runs from January 13 to February 11.
Brazilian winger Matheus Franca, 19, was handed his first start since his move from Flamengo in August in a £17m deal that could rise to £26m.
Franca, playing on the right wing, produced one of the best moments of the first half with a purposeful run, before James Tarkowski fouled him just outside the penalty area. Eze, though, fired the free-kick over.
Elsewhere, Jeffrey Schlupp had a low strike saved and Lerma shot over from 20 yards.
But a draw was a fair outcome as both sides had three attempts on target and seven corners apiece.
Everton, now without a win in five matches in all competitions, went close when Arnaut Danjuma had an attempt deflected into the side-netting and also forced Henderson into a good save.
Amadou Onana also headed over when well placed, but neither side could score and will have to do it again at Goodison Park later this month.
Palace and Everton, 14th and 17th respectively in the Premier League table, will both be in the fourth-round draw, which takes place at 19:50 GMT on Monday, 8 January before Wigan Athletic host Manchester United.
