Tosun made it four goals in his last three games for the Toffees with a double at the bet365 Stadium, including an 84th-minute winner to seal all three points against the 10-man Potters.
The January arrival had struggled for game time prior to his recent goalscoring run, but Allardyce believes that his spell out of the team is now beginning to pay dividends.
"You want the top-quality marksman to turn the game in your favour and I think Cenk has done that. He's adapted much quicker than lots of front men who come from abroad into the Premier League for the first time, particularly in January," he told reporters.
"Taking him out of the firing line, giving him the opportunity to get to know the players, do the extra training he's done, we're seeing the full benefits of that now.
"Goals have been a shortfall for us this season and if he's going to be the one that can get into double figures and turn a game like he's done, that would be great. He's the major reason why he won today."
Everton now sit ninth in the Premier League table having reached the 40-point mark.