Marie-Helene Premont of Canada took the silver and Germany's world champion Sabine Spitz took the bronze.
Danish racer Mette Andersen was stung by a bee on the second lap of the five-lap race and had a bad reaction. The left side of her chest swelled up and she had to pull out of the race and seek medical attention.
Dahle completed the five-lap 31.3km course in just under two hours to beat Premont by 59 seconds.
Dahle commented in her post race interview "I fell once and I damaged the gears which slowed me down a bit. I had to get off the bike and push on some of the steepest parts of the course."
Tune in to BBC1 tomorrow morning from 10.30am to see MBUK's own Oli Beckingsale and fellow Brit Liam Killeen battle it out for Olympic glory.