As the final descent approached Van der Breggen launched what looked like being the winning attack, opening up a 10-second gap over the chasing Van Vleuten and maintaining that advantage on the downhill.
But Van Vleuten did not give up and slowly reeled in her fellow Dutch rider, bringing the gap down to four seconds going into the final kilometre.
It looked for all the world like Van der Breggen would hold on, but one final ramp in the last 100m saw the 28-year-old blow up and Van Vleuten overtook just yards from the finish line.
The win caps an extraordinary two years for Van Vleuten, who recovered from a horror crash in the 2016 Olympics to win the World Time Trial title last September before dominating in the recent ten-stage Giro Rosa.
Speaking after her remarkable win, Van Vleuten said:
Last year was super nice but that was unbelievable. With 200m to go I thought I was going to come second but then I saw her dying. I knew I was in good shape but she's a really good cyclist. It was tough but so beautiful to win this way. The gap was small [over the last climb] but I know she's a good descender. I always kept on dreaming and believing in myself - I could've given up with 500m to go but I always believed it was possible. This win is really beautiful, together with last ear, winning the Giro Rosa on Sunday and then this, it's really high on my list.
The drama of the race will heap further pressure on ASO to expand La Course to a full tour. The 2017 edition saw the riders take on two stages (a half-hearted mountain stage followed by a staggered start time-trial style second stage) but the limited success of the format saw it ditched for 2018, with the race becoming a one-stage event.
While many saw that as a backward step, it has been argued that ASO treated this week's race as a trial run of having women's and men's races on the same route on the same day. And the success of Tuesday's event should result in the race being expanded in future seasons. No date on a decision has yet been set.
La Course by Le Tour de France results:
1. Annemiek van Vleuten (Mitchelton-SCOTT) 03:20:43 2. Anna van der Breggen (Boels-Dolmans) +0:01 3. Ashleigh Moolman (Cervelo-Bigla) +1:22