Everton produced a determined away performance to secure what could be a valuable away point with a 0-0 draw at Crystal Palace.
The Blues, who were forced to play the closing stages with 10 men after Holgate was sent off for a second bookable offence, went closest through Alex Iwobi’s well-hit volley in the first half before the returning Dominic Calvert-Lewin prodded agonisingly wide of the target after the break.
Palace’s best effort came via Eberechi Eze’s precise shot late on but Jordan Pickford was on hand to produce an excellent save to preserve a share of the spoils.
Calvert-Lewin, who had missed the previous 10 games, and Holgate came into the starting line-up as manager Sean Dyche made two changes from the side that started the home defeat to Fulham last time out.
There was a more familiar shape, too, with Demarai Gray returning into a wide role with Calvert-Lewin spearheading the visitors’ 4-5-1 starting formation.
Everton — in their changed strip of all yellow — were in no mood to be polite hosts, winning the toss and turning the teams around ahead of kick-off.
It set the tone for what would turn out to be a scrappy first half, with neither side able to establish a free-flowing rhythm and genuine chances falling few and far between.
Calvert-Lewin’s physicality was a clear weapon for Everton, though, as shown in the opening exchanges when Iwobi directed a clipped pass into the box and the Blues’ number 9 beat Marc Guehi in an aerial battle before glancing the ball on target via his shoulder — but it proved a comfortable save for goalkeeper Sam Johnstone.
At the other end, the lively Michael Olise delivered an inviting free-kick from the left channel and Jordan Ayew rose highest before heading high over the crossbar from eight yards out.
Olise threatened again with a purposeful run down the right flank but Vitalii Mykolenko tracked his every step and did enough to shepherd the France Under-21 international out of play for a goal kick as he threatened to penetrate penalty area.
On the other flank, Ayew was asking questions of Holgate. Pouncing on a hopeful ball into the right channel, the Palace forward dug out a cross with intended target Jeffrey Schlupp only able to head the ball high and back towards the edge of the penalty area, where Tyrick Mitchell blazed over with a wild effort.
The closest the deadlock came to being broken in the opening half came on 37 minutes, when McNeil’s second delivery into the penalty area — following a failed free-kick — was nudged clear by Mitchell but only as far as Iwobi, who connected with a venomous volley that forced Johnstone into a diving save at full stretch to his right.
Calvert-Lewin and McNeil threatened with ambitious long-range efforts — both easily saved by Johnstone — as the first half drew to a close.
Everton began the second period with more attacking intent but it was Palace who thought they had opened the scoring just before the hour mark. Guehi’s lofted pass released Eze down the middle and the winger made no mistake in lifting the ball over the on-rushing Pickford and into the back of the net.
Fortunately, the offside flag was raised and the score remained 0-0.
The Toffees remained positive and came within a whisker of scoring themselves five minutes later.
Palace defender Joachim Andersen failed to adequately deal with a long ball forward by Pickford, allowing Iwobi to pick up possession and release Calvert-Lewin into the penalty area. Everton’s striker cushioned the ball with a delicate touch while pirouetting to lose his marker before prodding an effort inches wide of Johnstone’s left-hand post.
While soaking up pressure, Roy Hodgson’s pacy frontline remained a threat on the break and went close through Eze with 14 minutes remaining. The winger worked himself a yard on the edge of the penalty area before opting for precision, with Pickford reacting excellently down low to his left to scoop it away to safety.
Everton were handed a blow with 10 minutes remaining when they were reduced to 10 men after Holgate was shown a second yellow card for a foul on Ayew in the right channel.
Lifted by their numerical advantage, the home side pressed in the closing stages but Everton toiled and held on for a draw.
Next up for Dyche’s men is the visit of Newcastle United under the floodlights at Goodison Park on Thursday evening (7.45pm BST).