The Toffees skipper completed their haul three minutes before time after Ross Barkley and Romelu Lukaku had fired Everton into a two-goal lead.
After overcoming a bright start from Newcastle, Everton seized control of the game and a first away victory of the calendar year saw them move up to fifth in the Premier League standings.
Osman hailed the well-rounded performance of his side and believes they are gathering momentum at a crucial point of the season.
"I think we've been scoring some decent goals this season, but to score three goals like that on the night was even more pleasing," he told Sky Sports.
"We've had back-to-back wins before tonight and it was important that we started to pick up points away from home to get us in the direction we're heading for."
Roberto Martinez's side are now just six points behind Arsenal - with a game in hand - and although Osman believes Everton are outsiders for a top four finish at present, he claimed they will not be giving up on their chase.
"We've got to play some of the big teams yet and we're vying for it ourselves, we're the outsiders at the minute but we'll keep ticking along," he added.
"It is important [to keep this momentum] but we concentrate on the next game, we did that tonight and it went well."