With incoming boss Sam Allardyce watching on from the stands at Goodison Park, Rooney scored from inside his own half in the 66th minute as he met Joe Hart's clearance inside the center circle and sent the ball straight in.
Asked if he had ever netted a goal better than that, the 32-year-old told BT Sport: "I don't think so.
"It's one of, if not, the best goal I've scored. I hit it as well as I've ever kicked a football. To make it my first hat-trick for Everton, I'm delighted."
Captain for the night Rooney's first goal came in the 18th minute as he headed in on the follow-up after his penalty was saved by Hart, and he slotted home his second 10 minutes later.
Jordan Pickford then saved Manuel Lanzini's spot-kick just before the hour mark, and after Rooney's outrageous effort from distance, Ashley Williams added a 78th-minute header.
The win, which moved Everton up from 17th to 13th in the Premier League, was only their second in eight matches since David Unsworth stepped up from the under-23s to take caretaker charge following the sacking of Ronald Koeman.
Allardyce, sat alongside Everton's major shareholder Farhad Moshiri and chairman Bill Kenwright at the game, will surely have taken great encouragement from what he saw hours after the club had announced he was to finalize terms on becoming their new manager.
Rooney said of Allardyce: "Of course he'll be pleased, but for us as a team, as a club, it was important for us to show some pride. As David Unsworth said, we've been hurting."
He added: "We've got to give thanks to David Unsworth. He's stepped in at a difficult time for the football club, he's a true Everton person.
"I'm delighted for him we've got this victory because it's an important win for the club but also for David Unsworth."