Valtteri Bottas came in second place for the fourth time this season while Lewis Hamilton's fifth-place finish meant he gave up his place at the top of the standings to victor Sebastian Vettel.
It's off to Provence in two weeks time, with Vettel now a point ahead of Hamilton in the drivers title race.
Mercedes team boss Toto Wolff, whose team still lead the constructors' standings, called it a wake-up call but Hamilton made clear that he was already aware of the threat.
"We all know they (Ferrari) have generally had a slightly better package all round, they've been doing a slightly better job so we've got to do more", the Briton told reporters.
"I've got complete confidence in my guys and I'm putting that energy towards them. It's unbelievable. I said yesterday how much this place means to Ferrari and to have a race like we had today is unbelievable", said Vettel.
"We have got to keep working, and keep pushing because Ferrari will falter if we can apply the pressure".
Hamilton was forced into making an earlier-than-planned pitstop, which compromised his race strategy, so Mercedes could remove some bodywork panels around his headrest to bring his engine temperatures down. Daniel Ricciardo (Red Bull) 20.892, 5. Other teams chose to have seven or eight sets of "hyper-soft" tyres at their disposal, but Mercedes asked for only five. They will need to have that resolved in time for the next race, the French Grand at the Paul Ricard Circuit at Le Castellet next week, a venue that has been off the calendar since 1990 and represents new ground for all the drivers. "I told them I don't think the race is over yet", said Vettel, who confirmed on the counter in his auto and with his team that he was only completing his 69th of the scheduled 70 laps. I was down on power, and every single lap I was on edge waiting for the power to drop away. "That's something we have to make sure we can take care of". The races are coming thick and fast now, with Austria and Britain on successive weekends after France in a triple-header before Germany and Hungary lead into the August break.
"This is a s**t result for us".
"I think we've got potential in this auto and when you guys are writing your stories, I think past year there was "oh, Mercedes have the best car" and all those different things, but ultimately I think we did the better job".
"I'm still here to win and still believe that we can. We have different communication systems and different languages at every track", he explained.