Van Aert launched his sprint from a good position and was able to pass Bol to secure the win after a hot pace was set by Team Sunweb.
"Yeah, it was a heavy finish," said van Aert. "It's maybe the most easy I ever did in a cycling race because there was no breakaway, not a high pace at all.
"The last hour was really hectic, there was a lot of wind. I knew this stage suited me and I'm just so happy that I got an opportunity from the team to go for it."
The biggest drama from the stage came after the finish, as it emerged that the race jury was taking a look at footage of yellow jersey-holder Julian Alaphilippe receiving a bidon with 17.1 kilometres to go, illegal under Union Cycliste International (UCI) regulations. Alaphilippe was penalised 20 seconds on the general classification and lost the yellow jersey as a result, with Yates moving into the overall lead.
An early attack from Kasper Asgreen (Deceuninck-Quickstep) was followed by Thomas de Gendt (Lotto Soudal) indicating that the Belgian squad wasn't in much of a mood for messing around chasing without help. The pair went back to the peloton and no one else attacked.
That was the way it stayed for the rest of the 183-kilometre journey from Gap to Privas. Once the peloton entered the outskirts of the town, with nine kilometres remaining, INEOS Grenadiers tried a brief push in the crosswinds.
There were some echelons formed, with Bauke Mollema (Trek-Segafredo) caught out momentarily before the peloton reformed as the teams prepared for the sprint.
The sprint was contested on a slight uphill, with the Team Sunweb sprint train doing a good job to string out the peloton and launch their sprinter Bol.
Van Aert launched around the outside of Bol, pipping the Dutchman in the throw to the line, with Sam Bennett (Deceuninck-QuickStep) closing fast from behind for third.
Bennett's third-placed finish was enough to propel him into the green jersey, holding a 9 point lead over Sagan.
The Tour de France continues tonight with a 191-kilometre stage from Le Teil to Mont Aigoual, with the broadcast starting from 9.00pm (AEST) on the SBS ŠKODA Tour Tracker App, then from 9.30pm (AEST) on SBS and SBS On Demand.
