The Ghanaian international netted his sixth goal of the season to earn a 1-1 draw in the Premier League and make his transfer fee of £2.5million look even more of a bargain.
Ayew joined the club in the summer from Swansea after a season-long loan in the 2018/19 campaign, which saw him find the net just twice at Selhurst Park.
Despite this, he has won over the fans with his work-rate and the importance of his goals, which have earned Palace 10 points this term.
Hodgson said: "I think the club is sensible because you need to know the type of players that suit your style of play and will help you.
"Then if you take other guys like Cheikhou Kouyate, James McCarthy, Jordan Ayew and Gary Cahill; they fit the profile of players that are prepared to knuckle down, work for the team and not seek personal glory, but to seek their glory through team performances.
"I suppose that is our mantra as a coaching staff. We might not have (Pierre-Emerick) Aubameyang, who needs one chance to score. We might need someone who might need a lot more chances, but what he might do is do what Jordan Ayew has done.
"Watching him is a testament to what we have tried to do with our limited resources to get the right people."
Palace were without Joel Ward (knee), Mamadou Sakho, Patrick Van Aanholt (both hamstring), Victor Camarasa (calf), Jeffrey Schlupp (hip), Andros Townsend (groin) and Christian Benteke (muscle) on Saturday.
Captain Luka Milivojevic also started a three-match ban against Arsenal and Max Meyer may join the aforementioned eight on the sidelines after he was on the receiving end of a terrible tackle from Aubameyang.
Hodgson expects the German to have some type of ankle ligament damage and although Palace anticipated a more aggressive Arsenal under Mikel Arteta, he did not feel they overstepped the mark.
"I didn't think they were particular nasty or dirty team to play, but if he wants to get them up the table he has maybe got to add that to the incredible quality the club has," he added.
"There is no doubt when they get the ball in the final third and that front four is on the ball, you can expect problems because they are such good technicians and capable of scoring goals."
Next up for Palace is a daunting trip to Manchester City on Saturday, but the last time they visited the Etihad they secured a shock 3-2 win in December 2018.
"We won there once," Hodgson joked. "It seems like a lifetime away, but we did win a game there and we dine out on that every now and again.
"They beat us here (this season), so on this occasion we are trying to avoid two defeats."