Redmayne finished just under two seconds ahead of Malachi Mitchell-Thomas, who had led by 10 seconds on lap two before his bike overheated.
The Laxey racer dedicated his victory to last year's winner Andy Lawson, who died racing at the Ulster Grand Prix.
Mitchell-Thomas set a new lap record on his final lap at 120.565mph.
Billy Redmayne had a seven-second advantage over eventual third-place finisher Rob Hodson from Wigan after the first lap, with Mitchell-Thomas third.
Mitchell-Thomas then surged ahead and had built up a 10-second lead before his bike overheated at the Creg on lap two.
The Horwich teenager lost 16 seconds after pulling over, before fighting back to finish just 1.9 seconds behind last year's runner-up.
The Laxey man, who has served three six-month tours Afghanistan, said: "I finished second to Andy (Lawson) last year and I want to dedicate this one to him.
"The conditions were really tricky over the Mountain but I just got my head down and cracked on. I have a lot of people to thank and it feels great to win."
Mitchell-Thomas, who broke Manx racer Tommy Clucas's 2004 lap record on his final circuit, said: "It was going great but the bike overheated on lap two and I was covered in water.
"I pulled over and it cooled down so I got going again but I couldn't quite catch Billy. We still have the Senior and there is more to come."
Hodson finished 12.2 seconds down in third.
Manx soldier Billy Redmayne won a thrilling three-lap Junior Manx Grand Prix in challenging damp conditions on Wednesday.