Two second half goals kept the current East Lancashire League champions in the hunt to retain their title.
But Rimington, according to manager Terry Braithwaite, remain an outside bet.
The first half was a rather drab affair, the home side struggling to play with any fluency on a soft pitch, and the visitors aiming to hit the ball over the defence to run on to.
However, that meant that the ball was in the Rimington half more than they would have liked.
But Dinsdale and Hartley were dominant at the back, and with Kershaw commanding his area, chances for the visiting side were kept to a premium.
In the second half, Rimington played with much more pace, urgency and inventiveness, getting Benfield more on the ball, and Robinson and Hickling getting round the back to set up opportunities for Blackburn.
But it seemed the Ossie keeper was going to have one of those days when he wasn’t going to be beaten.
Oswaldtwistle should have opened the scoring with just 20 mins remaining, as a good move resulted in a striker bearing down on Kershaw’s goal, but as the big keeper spread himself, he did enough to ensure the ball was lifted over him and also over the bar.
A change of formation, with Shaun Mansfield replacing the hard-working Robinson to play as a striker in a three-man attack, brought dividends immediately.
A flowing move saw Benfield find Fagan, and then Hutchinson and Walsh combined, finally giving Blackburn the chance he had been waiting for, and he forced the ball over the line to open the scoring on 78 minutes.
This made the visitors throw caution to the wind, and Kershaw had to save at the feet of an onrushing attacker to keep his side in front.
The game was finally killed off when Walsh grabbed the second, the ball being headed back across for him to head in.
Braithwaite was pleased with the points and the way his team stuck to their task: “Ossie made it difficult for us, they competed very well and we struggled for momentum, but we changed it and it paid off. Shaun went on and even though he is not a striker, it made then think about him which gave Dan Blackburn a bit more freedom, and that led to the goal.
“All we can do is try to keep winning and see if the pressure gets to The Ivy and Burnley Athletic.
“We have them both to play, so they will be crunch games, but I see their games against Read as pivotal.”