The victory lifted the Steel to four wins from six matches and, with the ANZ Championship at its midway point, Broughton believes her team is well-placed to make the play-offs.
"I think we can take a lot of heart from that [victory]," Broughton said.
"It was a very good result. We were resolute and never gave up.
"If you look at the table, I think we are in a good position [in the competition]."
Late last month the Steel suffered its heaviest defeat - a 17-goal drubbing by the Melbourne Vixens - but bounced back with a 61-52 win over the Mystics and strung back-to-back victories together for the first time this season with its win over the Tactix.
Broughton acknowledged the back end of the season looked tough, but warned her side had shown a lot of character and had continue to improve.
The Steel plays New Zealand's strongest franchise, the Magic, in Invercargill next Monday night and has two difficult encounters across the Tasman against the West Coast Fever and Queensland Firebirds.
It rounds out the tournament with a game against the talented Adelaide Thunderbirds in Dunedin on June 29 and the defending champion, the New South Wales Swifts, in Invercargill on July 4.
It also has very winnable games against the Mystics and Pulse.
The Steel suffered a setback before Saturday's opening centre pass, when Adine Wilson pulled up lame with a calf injury during a training session on Friday.
Broughton said it was not known how long the Steel captain would be off court but commended her side for stepping up in her absence.
"She has such a presence on court and it was a huge loss."
The wing attack has been in scintillating form and the Steel lost some direction without her.
The Tactix seized control of the midcourt battle through Julie Seymour and Maree Bowden.
The Silver Ferns duo outplayed counterparts Wendy Telfer and Liana Barrett-Chase in the first half.
Telfer, though, improved in the second half and manage to upset the Tactix's supply of ball at crucial times.
With Jodi Brown and Anna Thompson both shooting well, the Tactix took a 14-13 lead into the break.
Broughton re-jigged her defence, dropping Megan Hutton to the bench, moving Katrina Grant to goal keep, switching Sheryl Scanlan from wing defence to goal defence and bringing Erika Burgess on at wing defence.
The move did not reap immediate dividends, but Broughton showed faith in the combination which got better as the match progressed and ultimately delivered the winning of the game.
With the Steel trailing 46-45, Scanlan got a crucial tip with her away hand and rounded the ball in.
Daneka Wipiiti converted the turnover and the Steel scored off its centre pass to take the lead with about 90sec remaining.
It was a decisive blow and the sort of play that can help turn a season.
The Tactix had looked the hungrier of the two sides and played with the desperation expected of a side that realistically had to win to keep its semifinal prospects alive.
The home side led for most of the match and stretched the lead to seven goals midway through the third quarter.
Donna Wilkins started slowly but found her rhythm and with Wipiiti shooting superbly throughout, the Steel clawed its way back into the game.
For two netball fans the thrilling match was a dream come true.
Hannah Winters (17), from Invercargill, and Becky Corby (12), from Rangiora, were courtside watching the nail-biting encounter.
Both girls are supported by Make-a-Wish New Zealand - a charity dedicated to fulfilling the wishes of children with life-threatening illnesses - and got to meet Steel captain Wilson and Tactix captain Seymour.
"Fans like Hannah and Becky inspire you to get out there and lift your game," Wilson said.
"The whole team got a buzz out of knowing the girls were sitting courtside, cheering us on."
Hannah has overcome a liver transplant to play and coach netball.
But Saturday's narrow win left the committed Steel fan shaking with nerves.
"It was so hard to watch - I just wanted to run on to the court and help them out," she said.
Southern Steel 48 (Daneka Wipiiti 30 from 34, Donna Wilkins 18/22) Canterbury Tactix 47 (Jodi Brown 32/37, Anna Thompson 15/17).
Quarter 13-14, half-time 26-24, third-quarter 39-37.
