Brown's men halted their five-match losing run in sensational style, coming from 16-0 down to topple the champions with a third consecutive win at Headingley and climb back into the top eight.
"Hopefully this is the start of a good summer period for us," Brown said. "We fought really well and we should get a lot of confidence out of tonight."
Saints looked certain to register their worst run for 34 years after conceding three tries in an abject first quarter but their fortunes were transformed in remarkable fashion.
They pulled two tries back in six minutes before half-time through Louie McCarthy-Scarsbrook and Sia Soliola and ran in three more in a 10-minute spell early in the second half, two of them by winger Tom Makinson, who finished with 14 points.
Then, after Leeds threatened a late fightback, 18-year-old prop Luke Thompson, playing only his third Super League match, went over for the match-clinching try that lifts Saints back into the top eight and breathes new life into their season.
"I expected us to play well tonight," Brown said. "I didn't necessarily expect us to win but I expected a good performance. The first 20 minutes were disappointing and I wasn't sure where we were heading but in the last 60 we did really well. To come from 16-0 down against a good side like Leeds, you've got to credit to the guys."
Kallum Watkins, Joel Moon and Rob Burrow all touched down inside the first 20 minutes to give Leeds a comfortable lead but coach Brian McDermott said he never felt the game was won.
"We were in command but that was never the game so early," he said. "I was never feeling comfortable at 16-0.
"I'm not sat scratching my head wondering how we lost. We missed too many soft tackles at crucial times and it gave them a bit of momentum. Take away a couple of blunders near our try-line and it's more of a tighter scoreline. Saints are desperate and they're a decent team. There were two teams who wanted to bounce back. I thought Saints played better than we did, so credit goes to them."
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