Richarlison scored twice in his first Premier League appearance for 10-man Everton, but a late goal from Raul Jimenez helped Wolverhampton Wanderers salvage a 2-2 draw at the Molineux Stadium.
Everton have not lost a top-flight opener since 2011 and kept that run alive thanks to Richarlison, whom they purchased from Watford for £40 million in July and reunited with manager Marco Silva.
But Wolves used Jimenez's late equaliser to salvage a point in their first game in the top flight since 2011-12.
Richarlison, who had not scored a Premier League goal since Dec. 12 -- before Silva was sacked at Watford -- opened the scoring in the 17th minute when Michael Keane's free kick into the mixer fell to his right foot.
Everton were reduced to 10 men in the 40th minute as Phil Jagielka lost control of the ball and tackled Ruben Neves, sending the studs of his right boot into Neves' left ankle.
Wolves answered four minutes later when Neves scored from the resulting free kick, curling it from 19 yards into the top right corner past a diving Jordan Pickford.
Richarlison reclaimed the lead for Everton in the 67th minute, carrying the ball into the area after a quick pass from Cenk Tosun and using Connor Coady as a screen to finish right-footed from 12 yards.
But Wolves were resolute and answered in the 80th minute when Neves released Jimenez into the box and Jimenez slipped past Keane to finish from a header.