The Dutchwoman is bidding for a historic treble of 1500m, 5,000m and 10,000m.
Ethiopia-born Hassan, 28, produced a devastating final-lap sprint to win in 14 minutes 36.79 seconds, but it seems she required a little assistance to carry her over the finish line.
“Without coffee I would never be Olympic champion,” she joked.
Hassan’s gruelling schedule means she will have run in six middle- or long-distance races in eight days.
In her 1500m heat earlier on Monday, she had to recover quickly from a fall just after the bell, swiftly picking herself up to qualify in first place.
“I can’t believe it. It was terrible when I tripped,” she said. “When I fell down and had to jump up I felt like I was using so much energy. I couldn’t believe the feelings in my legs. All the energy seemed to leave me.
“I was so tired. Without coffee I would never be Olympic champion. I needed all the caffeine!”
Kenya’s two-time world champion Hellen Obiri claimed silver in 14:38.36, with Ethiopia’s Gudaf Tsegay taking bronze in 14:38.87.
Hassan has a little longer to recover for her next race – the second semi-final of the 1500m, which takes place on Wednesday.
She has won world titles in the 1500m and 10,000m, with a bronze in the 5,000m. (Courtesy BBC)