Mollema launched a long-range attack to surprise the punchier climbers, like Alejandro Valverde (Movistar), Tony Gallopin (Lotto Soudal) and Joaquim Rodriguez (Katusha), in the field.
Tony Gallopin (Lotto-Soudal) was second, followed by former race winner, Valverde.
Mollema caught Rodriguez on a late uphill attack, then raced away, opening up a gap that was good enough to win the race in 5 hours, 31 minutes.
"The last days of the Tour de France were really disappointing for me, and this was a good way to fight back," Mollema said.
"I recovered well from the Tour, and I am really happy to win, I have always loved this race and have always finished in the top 10."
"This is the first WorldTour classic I have won and have always wanted to be on the podium of this race and have one of those Basque hats, and now I finally have one."
Rigoberto Uran (Cannondale), then Adam Yates (Orica-BikeExchange), were the first to go on the offensive as the end neared.
Yates was then challenged by Rodriguez, 37, who rode his last "Klasikoa" after announcing he will retire at the end of the year.
But Rodriguez was caught up by Mollema, Valverde, double winner of the race in 2008 and 2014, and Gallopin.
Mollema broke away in the final descent and would never be caught up by the other three.
“I was a few places behind when Rodriguez went, and it was a narrow climb, so it was difficult to pass the other riders,” Mollema said.
“But I felt quite good and knew that I could close the gap in the last few hundred meters of the climb. On the top, we were four and Rodriguez slowed down a little bit, and I think that was the perfect time to go.
“I tried and saw I had a gap and then it was just full gas until the finish. I think with two kilometres more or less I knew I had it.
“I still felt I had some power in the legs, so I was not going to blow up, and when I looked back, I didn't see the second group. I felt I could keep it until the finish, It was a nice feeling, especially in the last few hundred metres.”
The race was the final dress rehearsal for many riders before the Olympics, which kick off on Aug 6.
"After the Tour de France, the Olympics are a big goal for me," Mollema said. "This will motivate me even more. I'm really looking forward to going there. We have a very strong team this year."