Hearts relinquished their hold on the Scottish Cup at the first hurdle last Sunday, but took a half-time lead on their return to Scottish Premier League action courtesy of Ryan Stevenson's 31st-minute penalty, his first goal since his August return.
Callum Paterson, an interval replacement for head-knock victim Stevenson, doubled the lead after 54 minutes and Aberdeen were frustrated by Jamie MacDonald, who made a number of sharp saves.
The Dons, it seems, cannot score against Hearts. Their wait to find the net against the men in maroon was extended to eight matches, the last strike coming in January 2010.
Hearts were on the defensive as the Dons, rejuvenated in almost exactly two years since losing Craig Brown's first match in charge at Tynecastle 5-0, began on top.
Jonny Hayes and Sutton exchanged early shots before Hearts, with Gordon Smith included up front alongside Sutton, found their feet.
Full-back Ryan McGowan's cross narrowly evaded his team-mates, Jamie Langfield blocked as Sutton attempted to turn in a crowded area and McGowan headed wide from a corner.
The Dons had chances too. Andy Webster made a block with Niall McGinn lurking and a Hayes cross went through to Jamie MacDonald, who then saved well as the winger cut inside to shoot with his favoured left foot.
Hearts were awarded a penalty when Andrew Driver's corner was directed towards McGowan, who, with referee Euan Norris in close attendance, was hauled down by Josh Magennis. Stevenson converted right-footed into the top left corner.
Stevenson required treatment before half-time as a result of a clash of heads and Paterson took his place on the right, but offered more width.
Paterson blasted wildly over from McGowan's knock down, but the 18-year-old found the net shortly afterwards.
Hearts burst down the right, Smith stumbled, but quickly regained his feet, to beat Joe Shaughnessy and cut the ball back for Paterson to drill the ball into the opposite corner. It was his fourth of the season.
Aberdeen pressed forward and MacDonald saved from Scott Vernon.
Jamie Masson shot over and his fellow substitute Declan McManus straight at MacDonald as Hearts absorbed the pressure once more, with Sutton a useful outlet.
Denis Prychynenko and Marius Zaliukas had long-range shots saved by Langfield and McManus failed to cleanly connect as Magennis' long throw dropped for him at the other end.
It summed up the Dons' fortunes, but Hearts were worthy of all three points.