After Aberdeen's Kari Arnason had hit the bar and Arvydas Novikovas had given Hearts a 24th-minute lead, Sutton scored his first goal since his summer move from Motherwell after 35 minutes at Tynecastle on Saturday.
The striker added his second after 52 minutes as the hosts claimed a morale-boosting first Scottish Premier League win of the season ahead of Spurs' Europa League visit on Thursday.
The Dons' most recent previous appearance in Gorgie was the 5-0 loss the day after Craig Brown's appointment as boss last December.
If Aberdeen were short of confidence that day, they appeared deflated once again after a third loss from four games this season - and they are still to score.
More can be expected of Hearts' next visitors in white.
With Tottenham's Premier League match with Everton postponed this weekend, Spurs assistant first-team coach Clive Allen took the opportunity to assess Paulo Sergio's Jambos from the Tynecastle directors' box.
Allen would have seen little to unduly concern Spurs boss Harry Redknapp as the scoreline suggested a dominance which was not really apparent in the contest.
Hearts' weakness defending set-pieces was almost exposed from the Dons' second corner after 11 minutes when Arnason, who was on trial at Tynecastle over the summer, saw his header palmed onto the crossbar by Marian Kello.
Arnason was allowed to shoot narrowly wide from 25 yards soon after as Hearts' defence backed off.
The hosts then ruthlessly took advantage of Youl Mawene's failure to clear a Danny Grainger cross to take the lead.
Novikovas was the beneficiary, controlling the ball inside the area before shooting left-footed inside the far post.
Aberdeen continued to create chances, with Darren Mackie heading wide from Rory McArdle's cross when he perhaps should have done better.
Hearts punished the miss on the counter attack as Sutton converted David Templeton's cross.
Aberdeen supporters had spent the first half indulging in tasteless chanting in relation to Hearts' initial support of convicted sex offender Craig Thomson over the summer, the full-back having subsequently joined FBK Kaunas in Lithuania.
Like Hearts, FBK Kaunas are owned by Vladimir Romanov.
But the second goal quietened the away end.
Novikovas was replaced by Rudi Skacel at half-time after picking up a knock towards the end of the first period, with Mackie going off for the Dons and Peter Pawlett coming on.
After missing a header from a Grainger cross, Sutton netted his second after 52 minutes following a defensive mix-up.
Templeton was tackled, the ball ran for Scott Robinson, who passed between two lines of Aberdeen defenders and Sutton ghosted behind them to tuck in.
Fraser Fyvie dragged a shot wide when Hearts failed to clear a cross from the left before Richard Foster's long-range shot was easily held by Kello.
Templeton then failed to connect with Jamie Hamill's cross at the other end as Hearts spurned the chance for a fourth.
Aberdeen made two further changes, with Ryan Jack and Josh Magennis brought on for Rory McArdle and Vernon, respectively.
But the Dons still struggled and Skacel was shoved over by Arnason on the edge of the area, presenting Hearts with a free-kick.
Grainger's effort hit the wall and Skacel fired straight at Gonzalez soon after.
Kevin McHattie made his debut in place of Ryan Stevenson and Eggert Jonsson was replaced by Ryan McGowan soon after.
Jonsson had required treatment after nipping in front of Magennis to deny the Dons striker a shooting opportunity as Hearts kept a clean sheet in a comfortable win.