Blackburn dominated possession but could not make a breakthrough against a stern West Ham defence as the Ewood Park clash ended goalless.
Rovers had the better of the play during the first-half but it was the visitors who had the best chance to break the deadlock during the first 45 minutes.
Carlton Cole muscled his way into the box and looked certain to finish off a fantastic run but his shot sailed over the crossbar.
Blackburn continued to dominate the second-half but did not create the chances to match their possession.
Substitute Junior Hoilett almost snatched victory for the hosts when he was played clean through by David Dunn but his delicate chip was just off-target.
The game began brightly with debutant Pascal Chimbonda's surging run down the left touchline resulting in James Collins being booked for a foul on Morten Gamst Pedersen.
Dunn, making his first league appearance since April, lofted over the ninth-minute free-kick which Chris Samba headed back across goal but the stretching Jason Roberts could not divert the ball
Samba was then involved at the other end as some neat interplay between Junior Stanislas and Luis Jimenez set up Cole, only for his shot to be blocked by the big Rovers defender.
The England striker was being kept on a tight rein by the centre-back but when he burst into the penalty area Samba slipped to leave Cole clear.
He had a narrow angle from which to shoot but curled his right-footed effort wide of the far post without drawing Paul Robinson into a save.
Chimbonda twice denied Jimenez with sliding blocks in the penalty area before Samba, who was proving to be major player at both ends of the field, fired over from the edge of the West Ham box.
Three minutes into the second half Cole lashed a 20-yard shot over Robinson's crossbar with Collins' shot from Mark Noble's left-wing corner also too high.
Roberts was becoming increasingly isolated up front and in an attempt to counter that manager Sam Allardyce replaced holding midfielder Steven N'Zonzi with Hoilett.
Gianfranco Zola's first change was to replace Jimenez with Kieron Dyer, who made only his 10th appearance for the Hammers since August 2007.
Hoilett's first involvement was to shoot into the side-netting from Dunn's reverse pass in the 68th minute before returning the favour only for the midfielder to shoot straight at Green from 25 yards.
Summer signing Nikola Kalinic made his home debut when he replaced Roberts with 16 minutes remaining.
But it was fellow substitute Hoilett who should have broken the deadlock in the 77th minute when Dunn picked him out during a swift counter-attack with an incisive outside-of-the-foot pass.
Green raced out to meet the youngster who tried an audacious 20-yard chip which landed on the roof of the net. It was the closest either side came to scoring on a disappointing afternoon.