Alex Revell squandered an early opportunity to put the League Two side ahead on Saturday before Andy Webster flashed a header over from close range after 30 minutes.
But Hearts took the lead two minutes into the second half when Sutton slotted home from five yards from Ryan McGowan's pin-point cross.
Revell headed just wide and recent signing Kieran Agard was denied by Jambos goalkeeper Jamie MacDonald late on.
Hearts, who have won three of their four pre-season games, open their SPL campaign at home to St Johnstone next Saturday.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.