The Heed fell behind after seven minutes as Marcus Kelly put the Poppies in front in a first half that saw the hosts on top.
The second 45 saw a paradigm shift however, with Gateshead controlling the game and drawing level through Toby Lees after 65 minutes before Joshua Kayode sealed three points with an injury time winner.
Speaking to gateshead-fc.com, Williamson was quick to hail his players’ mindset to come through and earn their first win of the season.
“I’m delighted for the lads,” he said.
“That is football in terms of we were probably at our worst in the first 45 minutes, but the character and resilience they’ve shown yet again has paid off today.
“In the last four games that hasn’t got us the three points, but it just shows you what lads we’ve got here.
“They’re honest, hard-working and extremely resilient and it’s very pleasing for that hard work over the course of the five games to pay off today.”
Nicky Deverdics was one of the Heed’s standout performers in the second half, coming off the bench and grabbing an assist as he helped to turn the tables on Kettering.
Williamson said that performance is exactly what the midfielder is capable of, adding: “His quality is undeniable, but he hasn’t had as strong a pre-season as everyone else so we’ve got to be careful with him.
“He came on today and he changed the game, you could see that quality with his deliveries and the composure to get his foot on the ball.
“He wants to play every game, every minute just like everyone else and he deserved the rewards today.
“The whole group are delighted for [Kayode] and the lads were buzzing in the changing room because he’s hard-working, honest and that’s exactly what we try and coach into him.
“Over the course of the five games he’s deserved that goal and hopefully it will be the first of many.”