With West Ham boss Avram Grant enduring another week of speculation about his future, it was an important match for both managers, and, after a woeful first half, it was Blackburn who made the breakthrough in the 51st minute thanks to the scrappiest of goals from Ryan Nelsen.
Defeat would certainly have been harsh on the visitors, who were easily the more creative side, and they got their reward when Stanislas fired an unstoppable shot into the far corner.
The point was not enough to lift West Ham off the bottom of the table but they did close to within two points of Wolves.
Staff at Ewood Park had spent all morning clearing the pitch, stands and surrounding areas of snow and their efforts were rewarded as the match was the only one of the scheduled 3pm kick-offs in the Premier League to go ahead.
Grant was forced into a change in goal after Robert Green underwent a minor operation to remove a cyst earlier this week, meaning a West Ham debut for 23-year-old Belgian Ruud Boffin.
It was the first time Green had failed to start a league game for the Hammers for almost four years, and Grant's problems continued to mount before kick-off as Valon Behrami, who had been a doubt, was replaced by Jonathan Spector at the 11th hour.
The first half was a poor spectacle, with Blackburn's bright start petering out and West Ham managing only sporadic bursts forward.
The first decent opening did not arrive until the 41st minute as Luis Boa Morte played in Frederic Piquionne on the left of the area but the striker fired his effort towards the near post and into the side-netting.
West Ham were by then looking quite dangerous and moments later it was Boa Morte on the end of a throughball. This time he did find the target, forcing Paul Robinson into a good block.
Half-time came at the right time for Rovers, who had a new energy about them in the second half and soon gained the lead.
A shot from the lively Mame Biram Diouf was deflected behind by James Tomkins and, from the resulting corner, the ball was cleared to Brett Emerton wide on the right.
The Australian did brilliantly to work space for a cross, which caused havoc in the West Ham penalty area. Poor defending saw the ball drop to Benjani Mwaruwari three yards out only for the striker to completely miss his kick.
Waiting was Nelsen, though, and, after his first effort was superbly saved by Boffin, the Rovers captain forced the ball inside the right post off his thigh.
It was tough luck on the rookie goalkeeper, who did all he could but was let down by the men in front of him. Grant responded by bringing on Carlton Cole and Stanislas for Pablo Barrera and Spector, while for Rovers injury saw Christopher Samba replaced by Phil Jones.
Cole was immediately involved, appealing unsuccessfully for a penalty after a challenge by Gael Givet and then poking his shot wide under pressure from Jones following good work by Kieron Dyer.
That proved to be the last involvement for Jones, though, as he limped off barely 10 minutes after coming on, with teenager Grant Hanley given his chance by Kean.
Blackburn and referee Mike Dean earned the wrath of the West Ham fans when they failed to put the ball out after Matthew Upson went down clutching his face, and in the 71st minute the Hammers defender almost took revenge in the best possible way.
This time it was the Rovers defence that did not deal with a cross but Upson curled his shot against the outside of a post. The Hammers created another decent opening moments later, Piquionne heading Stanislas' corner over the bar.
They certainly deserved an equaliser, and 12 minutes from time they got one.
Scott Parker, so often at the heart of West Ham's best moments, drove into the box and Givet could only divert the ball into the path of Stanislas, who smashed his shot into the far right corner.
Blackburn had been poor but they upped their level again and thought they had gone straight back in front only for David Dunn to be denied by an offside flag.
Both sides pushed for a winner and Morten Gamst Pedersen almost caught out Boffin with an audacious 40-yard free-kick, while the Norwegian had the final chance with another set-piece from the edge of the area but sent his shot just the wrong side of the far left post.