Jonathan Bairstow finished unbeaten on 63 as Yorkshire secured a five wicket victory to blow the title race wide open.
Chasing 209 for victory after Notts posted 413 all out in their second innings, Yorkshire slipped to 95-4 as Darren Pattinson made inroads but Bairstow and Rashid guided the visitors to victory.
Notts visit Old Trafford next week with the destinatiom of the LV= County Championship in their own hands but Yorkshire's challenge is now much more credible.
“We’re going to go into the final game with a lead and we have to stay in a positive frame of mind and try and win the game,” said Read.
“There was pressure in the game but I don’t think it affected this result and we’ll give it our all as we have done all season.
“Yorkshire played fantastically well although it was the worst toss to lose all season and I would like to think that we’d be celebrating victory if we had won it.
“That’s the nature of the pitches here and we don’t make it easy for batsmen and Yorkshire took advantage of seam-friendly copnditions on the first morning.
“The way the guys fought back was a commendable effort but I think the game was lost with the toss of the coin to be honest.
“Rarely has the ball swung and seamed so much as it did in that first morning but after that the pitch became a very nice batting wicket.”
After the match, Nottinghamshire Director of Cricket Mick Newell confirmed that bowler Charlie Shreck had been the subject of an approach from a rival county.