The Black Cats secured their top-flight status with a goalless draw with Arsenal away from home at the Emirates Stadium on Wednesday.
Brady, though, believes that the 2-0 victory over Everton away from home at Goodison Park earlier this month was decisive for Sunderland.
“Sunderland fans will have woken up this morning with a feeling of jubilation having secured their Premier League status with a 0-0 draw at Arsenal,” the 46-year-old wrote in her football diary in The Sun (Thursday, May 21 entry).
“That may have been the result which made it mathematically certain, but surely the victory at Everton a couple of weeks ago was the one that did the deed.”
The win against Everton on Merseyside must have come as a surprise to even the Sunderland fans.
The Black Cats headed into the encounter on the back of a 2-1 win against Southampton at the Stadium of Light.
Both of Sunderland’s goals came in the second half. Danny Graham broke the deadlock at the Goodison in the 53rd minute when he hung out a leg to meet a wayward Jordi Gomez shot, the ball sneaking in off the post via the striker's calf.
It was the 29-year-old's first Premier League goal since December 2013 and helped Sunderland become more confident in the game.
With five minutes of normal time remaining, former Tottenham Hotspur and West Ham United striker Jermain Defoe made it 2-0 to Dick Advocaat’s side.
Over the course of the 90 minutes, Sunderland had just 27% of the possession, took 10 shots of which three were on target, and earned one corner.
The win meant that Sunderland moved up to 16th in the Premier League table with 36 points from 35 matches, two points above the relegation zone with a game in hand.