The Hawks trailed by 20 points in the third quarter but finished full of running in their 14.15 (99) to 13.4 (82) victory at the MCG in front of 47,945 fans on Thursday night.
Gunston put Hawthorn in front with his third major - the 13th lead change of a see-sawing contest - approaching time-on in the final term and added another late to seal the result.
The Hawks piled on 5.5 to 1.1 in a dominant last quarter.
Newcombe tallied 31 disposals and nine clearances, lifting after half-time when Hawthorn took over at the coalface to post a second-straight win, following a first-up hammering from GWS.
"They're a very good side and we had to really earn the win. It felt like a well-earned game," Hawks coach Sam Mitchell said.
"I couldn't be more proud of the effort the players put in. There was an intensity about the whole game, right to the last five seconds.
"So for our players to put together 120 minutes of really high-intensity footy was a good sign."
Dylan Moore (22 disposals, three goals) and Josh Ward (27 disposals) were also busy for Hawthorn, Jack Ginnivan (22 disposals) had a say after half-time and Nick Watson (18 disposals, one goal) shone late after shaking off separate knocks to his hip and head.
Key defender Tom Barrass played an important role keeping Charlie Curnow quiet, after the Swans' spearhead kicked two early goals on Josh Battle.
Chad Warner (27 disposals, six clearances) and Callum Mills (29 touches) fought hard for a Sydney side that was without star duo Errol Gulden and Isaac Heeney through injuries.
Logan McDonald kicked three goals for the Swans, including a controversial major that put them in front during the final quarter, awarded a mark and 50-metre penalty after Josh Weddle got a hand on the ball.
But the Swans were monstered in the contest after half-time and ultimately overwhelmed, with the loss ending their strong start after big wins over Carlton and Brisbane.
"To lose in all areas of the ground is something we need to look at," Sydney coach Dean Cox.
"It's really disappointing. Against really good teams you can't fluctuate to that level.
"To Hawthorn's credit, they ramped it right up and won the ball back in dangerous spots and then provided a lot of energy from that."
Hawthorn and Sydney both have an early-season bye next week before resuming in round four.
