Alaphilippe beat Ben Hermans – who usually rides for the Israel Cycling Academy, but is part of a Belgium national team at this race – and Pannon's Attila Valter to take the stage, and now leads the five-day race by 11 seconds from CCC's Jan Tratnik.
"It poured with attacks in the closing kilometre, but I marked every single one of them, and, as I still had plenty left in the tank, I kicked out with the finish line in sight," said Alaphilippe.
"The yellow jersey came as a bonus – a beautiful one – and I would like to keep it until the end, but we must first see what Friday's stage brings."
The victory came the day after Alaphilippe's teammate Bob Jungels had won the prologue time trial, taking the team's 62nd win in 2018, which was also a new record for the Belgian team, beating their previous 2014 record of 61 wins.
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The Norwegian was part of a day-long breakaway with Wallays and Jetse Bol (Burgos-BH), but when Bol dropped out of contention with just seven kilometres to go, and as the peloton bore down on them, Bystrøm opened up the sprint. Wallays waited and then passed him with a well-timed effort.
"It was close in the end for the win, but unfortunately I had to settle for second," the 26-year-old said on his team's website.
"Wallays was very strong in the breakaway, and we had cooperated well until the last two kilometres when he decided to sit up and I had to pull us to the line. Unfortunately, that decision resulted in me coming second.
"I thought we were tactically strong in the breakaway, riding quite easy in the first part," continued Bystrøm. "Then in the last 50km we agreed to go full gas and play with the peloton a bit, which worked out pretty well in the end.
"Of course I'm very disappointed right now – but at least I was there and fighting for the win."
With three stages left until the Vuelta ends in Madrid, Bystrøm may yet get another opportunity.
"Close but no cigar," he wrote later on Twitter. "Thanks for all the messages. I can guarantee I'll keep trying."
The 27-year-old currently races for the Roompot-Nederlanse Loterij Pro Continental team, which is set to merge with Veranda's Willems-Crelan to become Roompot-Crelan next year. But Van Goethem will leave all of that behind him as he moves to the Belgium WorldTour team for 2019.
"Being part of a WorldTour team is the highest achievable goal for every rider, so I am definitely looking forward to next season," Van Goethem said in a Lotto Soudal press release.
He's expected to strengthen the team's Classics squad, in particular, and is ready to work hard in a domestique's role.
"I hope my experience in the peloton will be a surplus for the team," said Van Goethem, who turned pro with the Continental Metec-TKH team in 2013, and has been with Roompot since 2015.
"After having participated in the Classics for a few years, you know the crucial spots on a certain course, and you know where you must be in the front to be able to play a role in the finale.
"Positioning is essential in the Classics, and I can certainly help the leaders with that. In that way, I hope and think I can bring added value to the team. It will certainly be an entirely new experience, and the WorldTour level is obviously a higher level than I am used to, but I'm really looking forward to supporting the team and making progress in a new professional environment," he said.
The Pro Continental team will be called Vital Concept-B&B Hotels in 2019, with team manager Jérôme Pineau having secured the backing of the Brittany-based hotel chain.
Pineau announced the news in a quirky video on Twitter – titled, "You won't believe what this dog is about to do!" to grab your attention – which French speakers will enjoy.
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