Tony Pulis’ men always looked the more likely to create something in a nervy encounter and could have had a penalty in the first-half when Ricardo Fuller was brought down in the box by Christopher Samba, only for referee Howard Webb to wave away the protests.
Liam Lawrence went close from a tight angle in the second half, when his fierce drive was tipped over the bar well by Rovers keeper Paul Robinson.
It was Lawrence who netted the decisive goal on the 75th minute, cutting inside Gael Givet before sending a left-footed strike past Robinson from eight yards out.
The win makes it seven games unbeaten at the Britannia Stadium for Stoke and moves them one point away from the magical 40 point mark, while Blackburn have slipped to 17th and are now just three points outside the relegation zone.
Theo Walcott feels there is still a lack of confidence among the Everton players despite their 1-0 win over Newcastle on Monday night.