Meintjies bridged across to the leading duo of Samuele Battistella (Astana) and Jimmy Janssens (Alpecin-Deceuninck) and dropped them both in the final 2 kilometres to ride solo in to the finish, as Battistella held on for second and Edoardo Zambanini (Bahrain Victorious) took third.
Just six weeks after he finished second on Alpe d'Huez in Stage 10 of the Tour de France, the South African looked unstoppable on the brutal gradients of Les Praeres to step on his first ever WorldTour podium.
“It’s something special and still needs some time to set in," Meintjies said after the stage.
"I’ve actually never been on the podium of a World Tour race so this was one of my main goals before stopping my career.
“The last few days in the mountain finishes I wasn’t quite fast enough to finish with the GC guys. If I can’t get a result that way then the best is to go in the breakaway.
"It worked out perfectly today. I was quite lucky. My team controlled it quite good in the start and I tried one time and I picked the right breakaway.”
Evenepoel was next over the line in fourth after a very strong performance, QuickStep-AlphaVinyl controlling the stage before the Belgian launched a surging attack in the last 3 kilometres to open big time gaps on every rider in the top 10.
The 171 kilometre stage saw constant attempts to get in the breakaway over the first 40 kilometres before a group of Battistella, Zambanini, Dylan van Baarle (Ineos Grenadiers), Meintjies, Filippo Conca (Lotto Soudal), Janssens, Australian Rob Stannard (Alpecin Deceuninck), José Manuel Diaz Gallego (Burgos-BH) and Simon Guglielmi (Arkea Samsic) managed to go clear.
The break worked together to keep the peloton away throughout the day, the gap going out to as much as five minutes as Alpecin duo Janssens and Stannard protected Australian teammate Jay Vine's KOM lead on the four climbs throughout including the Category 1 Mirador del Fito.
QuickStep were on the front of the trailing peloton keeping the pace high with Evenepoel in good position all day as Julian Alaphilippe took the front on the technical descent into the final climb with the break's advantage at 3 minutes and 38 seconds.
Battistella and Janssens attacked from the break with 10 kilometres to the summit finish, but the latter refused to do turns on the front allowing Meintjies to catch and pass them on the climb en route to victory.
Evenepoel's late attack saw him extend his lead to 1 minute and 12 seconds on second-placed Enric Mas (Movistar) and 1 minute and 53 seconds to third-placed reigning champion Primoz Roglic (Jumbo-Visma).
The Belgian now has the chance to recover on the rest day before starting Stage 10's Individual Time Trial as the favourite for the victory in another chance to flex his muscle on the other contenders.
La Vuelta takes a rest day before resuming on Tuesday night with Stage 10, a 30.9 kilometre individual time trial from Elche to Alicante. Watch the action LIVE from 11pm (AEST) on SBS and SBS On Demand.
