Arsenal missed the chance to climb above North London rivals Tottenham as they slumped to a 1-0 defeat at Everton in a game that saw them create few chances.
Everton made the breakthrough after 10 minutes when Jagielka, in the Arsenal box at a long throw, finished at the near post when the ball fell to him at close range.
Everton soon attacked again, a cross half-cleared before Idrissa Gueye slashed a wild shot out for a throw.
Arsenal were struggling to make an impact and had more concerns when Lacazette collided with Gomes and went down in pain, but the forward was able to continue.
Gomes found Sigurdsson on the edge of the area but he shot straight at Bernd Leno, and then Sokratis did well to cut out Richarlison's low cross from the right.
Arsenal boss Unai Emery made a double change at half-time, bringing on Pierre-Emerick Aubameyang and Aaron Ramsey for Sead Kolasinac and Mohamed Elneny, and Ramsey lofted over after Jordan Pickford's uncertain punch.
Ramsey was brought down by Gomes, who was booked, and fired wide as Arsenal showed signs of improvement from their tepid first-half performance.
Sigurdsson's dipping strike flew over as Everton responded, and after Lacazette put a header too close to Pickford the home side almost struck again when Leno saved well from Bernard.
Everton were beginning to recover their earlier verve as the game approached its final 20 minutes, Gueye having a shot blocked inside the area and Richarlison steering off target.
Henrikh Mkhitaryan fired narrowly past the post as Arsenal tried to up the tempo again, and then Richarlison, with time and space inside the area, skewed a shot horribly wide when he should at least have tested Leno.
Shkodran Mustafi was booked for bringing down Calvert-Lewin, the challenge sparking angry words between the two managers, and Nacho Monreal soon followed him for dissent as he disputed the award of an Everton corner.
Bernard made way for Ademola Lookman, Sigurdsson then replaced by Tom Davies as Everton held their lead through five minutes of added time to move above FA Cup semifinalists Watford and into ninth place.