A perfectly weighted pass from Ricardo Fuller released Whitehead, but the midfielder could not beat Robinson.
The hosts lost the influence of the in-form David Dunn after 31 minutes, Roberts filling the void left when the club's leading goalscorer limped off with a calf injury.
And it was Stoke making most of the headway now, with Robinson called to make a second important save, this time from Lawrence after the ball had somewhat fortuitously rebounded into his path off Sidibe.
Australian midfielder Grella came into the Blackburn line-up immediately after half-time after Andrews had become the club's second victim of a calf strain.
Draw a fair result - McDonald
Stoke had their best period of the match, Andy Wilkinson catching Givet napping before firing his shot wide.
Fuller was making a nuisance of himself and when he found Whitehead after a penetrating run, the striker completely fluffed an excellent opportunity.
Blackburn finally woke up from their slumber, Ryan Nelsen connecting well with a bicycle kick saved by Thomas Sorensen, before Nzonzi drove a left-footed volley on to the upright.
The visitors were not settling for a point, sending on former Blackburn player Beattie for the final 20 minutes.
Fuller remained a threat on the right, and his dangerous cross found Beattie on the edge of the six-yard box. But the striker needed a touch before shooting and yet another chance had gone begging.
In a frantic conclusion, Blackburn created plenty of dangerous openings but the final ball tended to go astray.
Neil McDonald (Blackburn): "The boys kept on going, and were trying to win the game right up to the last minute which was good. We've said we want to make people come here and work for the points and Stoke have definitely done that.
"For us, it's definitely a point gained against a side who are very hard to beat. I spoke to Sam [Allardyce] this morning. He's gone through the operation and is fine.
"I've enjoyed the experience."
Stoke boss Tony Pulis: "It was pretty end-to-end at times, both sides had really good chances - unfortunately for us we never took ours.
"We can defend a little bit better at times but going forward we were really a threat. Our goalkeeper had a fine game, I think Thomas [Sorensen] is as good as anyone in the league.
"I think we are a lot more cagey away from home than we were last year."
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