The forward, signed from Barcelona for an undisclosed fee last month, was on target in a 2-1 defeat against Schalke on Tuesday and struck again at Ewood Park on Sunday with a well taken left-foot finish to thwart the Championship side.
Jordan Rhodes had put Blackburn in front with a first-half header and they looked set to claim a Premier League scalp until Bojan, on as a half-time substitute, denied them.
Stoke boss Mark Hughes picked a strong side to face his former club, with new signing Phil Bardsley making an appearance alongside Ryan Shawcross, Robert Huth and Marc Muniesa in the back four and first-choice goalkeeper Asmir Begovic playing the first half.
Striker Mame Biram Diouf, another new recruit, was handed a start against the club where he spent a season-long loan spell in the 2010-11 campaign.
Full-back Bardsley wasted no time in making an impact as he swung over a cross for Peter Crouch 12 minutes in and the big striker headed against the foot of the post.
Jon Walters fired over the crossbar after good work from Diouf two minutes later, then Matt Kilgallon made a great block to ensure a Diouf strike went behind for a corner.
Blackburn also looked threatening going forward and Josh King headed just over the crossbar before Craig Conway picked out Rhodes with an inviting cross and the Scotland striker beat Begovic with a glancing header eight minutes before half-time.
Hughes made three changes at the break, with Thomas Sorenson, Bojan and Stephen Ireland replacing Begovic, Crouch and Marko Arnautovic.
The Premier League side went close to an equaliser just two minutes into the second half, when Walters headed a Charlie Adam corner over the crossbar.
Rhodes could have doubled Rovers' lead midway through the second half, but he headed King's cross over and he was made to pay when Bojan levelled a minute later.
The former Barca man picked up a pass from ex-Rovers midfielder Steven Nzonzi and flashed a left-footed strike into the bottom corner from 25 yards out.
Stoke finished strongly and Rovers goalkeeper Paul Robinson had to be alert to keep out Huth's close-range strike three minutes from time after Diouf had cut the ball back, but Stoke were unable to end their wait for pre-season win.
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