After a tight and tense first period, Crouch broke the deadlock with a stunning volley from 30 yards out on 59 minutes.
The England striker took one touch from substitute Jermaine Pennant's cushioned header before thumping a volley over the visiting keeper Joe Hart, who could not get a mitt to it despite being at full stretch.
Roberto Mancini's side needed a win to move two points clear of Manchester United - who host Fulham at Old Trafford on Monday night - but were forced to settle for a draw with Yaya Toure scoring the equaliser from a deflected drive on 76 minutes.
The Ivory Coast player hammered in a speculative shot from 35 yards that hit Ryan Shawcross before flying beyond the Stoke goalkeeper Asmir Begovic.
City are top of the table on goal difference from their city neighbours United, who will move three points clear with a win over Fulham.
Stoke were well worth their draw after a trademark performance of real energy throughout the evening.
Tony Pulis's side are one of only two clubs who are unbeaten at home this season against the Premier League's top five clubs. The other is Manchester City.
The visitors went into the match without Sergio Aguero, who apparently picked up an injury before the match. They certainly missed the forward with Carlos Tevez providing little of note when he replaced Gareth Barry on 74 minutes.
The best chance of the opening half hour fell to visiting forward Edin Dzeko, who headed over despite finding himself unmarked from Gael Clichy's delivery.
Pablo Zabaleta was forced to knock the ball off his line on 38 minutes after Shawcross had headed on Matthew Etherington's corner.
The second half began with Begovic saving at the feet of Dzeko before doing likewise in diving to keep out a long-range shot from Samir Nasri.
The game finally opened up in the dying moments with Manchester City pushing for the winner but continuing to lack real width. Stoke substitute Wilson Palacious saw a swerving effort dip over the bar on 87 minutes before Yaya Toure crashed a shot over the bar, but there was to be no further scoring.
City's patchy away form - they have collected 12 points from a possible 30 since thrashing Man United 6-1 in October - may yet prove pivotal in denying them the league title.
They remain without a win at Stoke since the home side were promoted to the Premier League four years ago.