Ghana forward, Jordan Ayew, has expressed his delight after scoring on his return from suspension.
The Swans had trailed to a Kyle Naughton own goal, but Carlos Carvalhal's side were back on level terms in the second half with Ayew controlling Tom Carroll's pass before firing into the far corner.
That was something an Everton side grasping for any kind of fluency allowed them to do and Jordan Ayew - back in the side following a three-match ban for his red card in last month's 0-0 draw with Huddersfield Town - crowned an enterprising display with a fine 71st-minute finish.
The result moved them onto 33 points from as many games - five points clear of third-bottom Southampton.
Jordan Ayew then linked wonderfully with his brother Andre, but he could only fire straight at Everton goalkeeper Jordan Pickford.
Seamus Coleman found Yannick Bolasie unmarked, but Lukasz Fabianski was equal to the winger's drive as well as Gueye's follow-up effort.
Pickford showed assured handling to deny Tom Carroll from a long throw early in the second period and the England global did well to parry behind from Andre Ayew at close quarters in the 51st minute.
Allardyce had angered Wayne Rooney by withdrawing him with more than half and hour left of the Merseyside derby the previous weekend, but the former England captain retained his place in the Everton side.
Everton were nearly back in front four minutes later when the stretching Coleman directed Tosun's cross against the bar from just five yards out.