The 36-year-old striker reached his century early in the game from close range, and celebrated in nostalgic fashion with his trademark robot celebration.
Crouch was impressive throughout the game, but he and Marko Arnautovic spurned chances to extend the hosts' lead in a dominant first-half performance before a Ryan Shawcross own-goal salvaged a point for Everton.
It was initially chalked off for offside, only for the decision to be reversed after referee Craig Pawson correctly ruled that Seamus Coleman's strike had struck the Stoke skipper and not Romelu Lukaku on its way into the net.
Stoke are now four league games unbeaten while Everton are six in the top flight without defeat.
The hosts were fastest out of the traps and Crouch reached his ton after just seven minutes when he slid home at close range from a pinpoint Arnautovic pass.
Everton's defence, watertight in their last three league games, were caught napping by a hopeful long ball that freed the Austria international on the left-hand side of the penalty area.
The veteran striker went agonisingly close to making it 2-0 after 25 minutes, catching Arnautovic's cushioned header sweetly on the volley, only to see his strike whistle past the post.
Joel Robles then charged down an Arnautovic effort as Stoke continued to dominate.
Everton struggled to match Stoke's intensity and were fortunate to draw level five minutes before the interval thanks to Pawson's change of heart.
Ronald Koeman introduced James McCarthy for Mason Holgate at half-time, abandoning his side's 3-5-2 shape, making Everton much more effective in inhibiting Stoke's attacking play.
Stoke were limited to two audacious Charlie Adam attempts from long-range to catch out Robles, and Crouch headed over just after the hour.
Mark Hughes brought on Saido Berahino for his Stoke debut in the 66th minute, though it was Everton's January signing Ademola Lookman who made an immediate impact from the bench, forcing Lee Grant into a smart save at his near post.
Both teams had chances to win it inside the final five minutes.
Berahino almost marked his debut with the decisive goal, lifting the ball over an onrushing Robles only for Ramiro Funes Mori to head to safety from below his bar.
His team-mates then owed thanks to Grant for safeguarding the point, improbably clawing away a goalbound Tom Davies header in the final stages as both sides had to settle for the a draw.