Pedrosa has 83 points after the fourth leg of the 18-race championship and leads Marquez by six points while Spaniard Jorge Lorenzo, a disappointing seventh on Sunday, is on 66 points.
It was Pedrosa's second victory in a row after he rode to the limit in tough conditions.
"It has been a great race for me because I didn't expect it," he told Eurosport.
"I always have problems here, with the temperature, the tyres are cold for me and I never get good grip. Last year I struggled a lot in the same race conditions but today I got some good grip on the tyres, especially in the front, so my braking was good.
"When I was in front I made a couple of mistakes, almost ran out twice and was on the limit."
Marquez, who started on pole as world championship leader, fell behind early in the race but produced a skilful performance to end up on the podium - a result he did not expect either.
The 20-year-old prodigy made a few mistakes, almost crashing once while fighting for position with Lorenzo but eventually managed to focus on his own performance.
"At the beginning and in the first laps the feeling was not so good," he said.
"I was struggling a lot to get rear grip, I nearly crashed many times. I went wide one time so I didn't expect to finish on the podium.
"But then I was focused on my race, tried to do my best and step by step I went towards the front."
Nine-times world champion Valentino Rossi of Italy skidded out on a curve 11 laps from the finish and finished 12th.
Crutchlow, however, managed to stay on the bike this time.
The Manxman had a medical before the race to check whether he was fit after he suffered a small fracture in his shinbone in a crash during a free practice session on Saturday.
"It's nice to finally get that podium. Hopefully from now on we can be injury-free. I knew Dovvy (Italian Andrea Dovizioso) would crack in the end with some pressure," he said after his best MotoGP result.
"He was slowing up quite a lot and he let Dani get away which was disappointing but I was happy enough.
"It was a difficult race. I couldn't see anything, that was the main problem. When you are behind the rider the stuff sticks to the visor so whatever Dovvy was spraying up, it was like mud and it was stuck to the visor and I couldn't see much," Crutchlow, who is now fourth in the world standings on 55 points, added.
There was more cheer for Britain when Scott Redding won the Moto2 race riding a Kalex.
Maverick Vinales led a Spain/KTM one-two-three when he won the Moto3 race.