Ryan promised to donate AU$500 to the bushfire relief effort in his native country for every save made in the Premier League this weekend and his defenders were also in charitable mood as they conceded a slew of chances.
Everton's Theo Walcott had two penalty appeals turned down in the opening 20 minutes before Richarlison broke the deadlock seven minutes before half time, making a quick stop and a tight turn in the box before curling in his effort at the far post.
"A fantastic goal from Richarlison, he has fantastic qualities. He can play everywhere," Everton manager Carlo Ancelotti said of his Brazil striker.
Leandro Trossard hit the woodwork for Brighton early in the second half while Dominic Calvert-Lewin thought he had added a second for Everton but VAR ruled he handled the ball when scoring and the goal was disallowed.
Brighton brought on experienced striker Glenn Murray but despite some decent chances for the 36-year-old, the visitors could not find the net and Everton hung on for the win.
"We tried, we put a lot into the game, the effort was there and we hit the bar but we didn't do enough to get that goal," Brighton boss Graham Potter told the BBC. "The difference was a great finish and we were not able to execute that today."
Everton's Ancelotti was not suprisingly a lot more satisfied than his opposite number after the final whistle.
"For 60 minutes the performance was good, at the end it was normal to suffer a little bit at 1-0 up. We suffered but we were determined to have three points at the end and this is the most important thing," the 60-year-old Italian said.
The Merseyside club are 11th with 28 points from 22 games, while Brighton stand 14th with 24, four above the drop zone.