Haig launched the decisive move from the early breakaway with 15 kilometres to go with van Baarle following the Australian's attack.
The pair worked well together to distance their erstwhile companions and came into the finish together, with van Baarle jumping first in the sprint and holding off Haig to take the win.
“The plan was to go in the breakaway and for Gianni and me to try and help Wout (Poels)," said van Baarle, "but it ended up a little bit differently."
“I'm so happy as this week had so many ups and downs. Everyone knows what happens to Chris (Froome, who crashed during the recon of Stage 4) and the team did a really great job with that. Obviously what happened to Chris affected us, it was a shock and it changed our line up. But we stayed together and showed that we are ready for the big race.
“In the past I really struggled in this race, so I trained and worked to be really good here and this win comes out of it.”
Haig wasn't too downbeat despite coming so close to a breakout WorldTour victory.
“The plan wasn’t necessarily for me to go in the breakaway but to get one of us guys in the breakaway if it was a decent size," said Haig. "It just happened to be quite hard at the beginning and I was in a good position, I saw the move going away and I jumped into it.
"The original goal was for me to try and stay there and try and help Yates move up the general classification but once I heard that he had pulled out, then I changed my focus to seeing if I could win the stage."
“I thought I should be there or thereabouts, looking at the other guys in the break, but I knew there would be a few that would be quite hard to get rid of in the end. Van Baarle was super strong and unfortunately I couldn’t get rid of him."
The battle between the main contenders didn't eventuate, with Fuglsang's nearest competitor Adam Yates (Mitchelton-Scott) dropping out midway through the stage and most of the other big names staying together on the run into the relatively easy finish.
"I was expecting a day that was harder than it turned out to be," said Fuglsang, "but my team did a perfect job as they controlled the race in the best way possible. A group went away with just one rider who was within 6 minutes in the GC, so there was no stress.
"I could just sit in the wheel of my teammates and they brought me all the way to the finish line. This victory for me is special because now I could actually ride in the yellow jersey, as in 2017 I won the race on the final day."
"I look forward to the Tour de France, I think I’m on the right way and until now it’s already been a great season for me and Astana. This year everything seems to come really easy and perfect, there is no stress and the atmosphere is fantastic."