Gower, an 18-year-old from Chichester, set up a comfortable lead with a mature, smart first run which allowed him to consolidate in his second run, finishing with an aggregate 1.2 seconds cushion over TJ Baldwin from Norfolk.
Scot Dougie Crawford, winner of the super G and downhill, finished third.
“I am so pumped I am really just over the moon.” Gower grinned. “I skied smart on the first run which gave me a big lead going in to the second run. I really focused on working hard, not taking any unnecessary risks, skiing the right line on the right snow. It worked out well.
"The second run was in difficult conditions which I don’t really excel in, so it was nice to come through the finish and see that I had won.
"I never thought about winning before I started today, but I did know I have the capability to win races, especially giant slaloms, before this. But this is the first race I have ever won since I started as a senior. So this is a really, really big day for me.”
Teenager Natalie Beattie became the new British women’s slalom champion.
Beattie, who hails from Arbroath but lives in Courchevel where both her parents are ski instructors, secured her first big British title when she put together two composed, confident runs as pre-race favourites Alex Tilley and Charlie Guest both crashed out of contention.
Tilley, leader after the first run, looked to be on course to win until she lost control just five gates from the finish line.
"It is really nice to win as this is the first time I have won anything at the Seniors. I had two good runs, but an especially good second run. It was unfortunate that Alex and Charlie both skied out. I made a couple of mistakes but it was OK in the end.” said 18-year-old Beattie.
1 Natalie Beattie (Courchevel) 56.09 secs, 54.89 secs 1min 58.98 secs, 2 Natalia Harte (Pila/Kent) 57.87, 56.26 1:54.13, 3 Rachelle Rogers (Hampshire) 58.56, 56.81 1:55.37, 4 Alice Macaulay (Surrey) 58.55, 58.69 1:57.24 5 Darcie Mead (Kingston upon Thames) 59.74, 57.90 1:56.46
1st Non British Team: Alice MacAulay, 1st under 18: Rochelle Rogers.
Men’s Giant Slalom:
1 J Gower (Chichester) 1:11.49, 1:16.21 2:27.70, 2 TJ Baldwin (Norfolk) 1:13.12, 1:15.78 2:28.90 3 Douglas Crawford (Bearsden, Glasgow) 1:15.28, 1:16.61 2:31.89, 4 R Bullen (Blackpool) 1:17.60, 1:17.67, 5 Roy-Alexander Steudle (Berkshire) 1:17.44, 1:18.12 2:35.66
1st Non British Team: Billy Major, 1st Under 18: Laurie Taylor.