The attacker pounced from close range in the 49th minute to help Terry Butcher's men close the gap on the Scottish Premier League's top six.
It was Inverness's second consecutive 1-0 league win against a team sitting third in the league before kick-off, having seen off Motherwell in their last outing.
Caley Thistle also extended their unbeaten streak to six games, while ending the Edinburgh club's own six-game undefeated run in the process.
Jamie Hamill came closest for Hearts when he hit the crossbar in the opening stages and the visitors will be frustrated they did not have a late penalty as they slumped to a ninth defeat of the campaign.
The game went ahead after referee George Salmond inspected the pitch at Tulloch Caledonian Stadium an hour before kick off
Seven of Caley Thistle's midweek Scottish Cup heroes were replaced by manager Terry Butcher.
Defender Kenny Gillet, who missed Wednesday's 3-1 extra time win at Dunfermline, was restored to the side, alongside on loan centre back Steve Williams, who made his full debut.
Goalkeeper Ryan Esson recovered from a groin strain to replace Northern Ireland international Jonny Tuffey, who dropped to the bench.
Sutherland, Nick Ross, David Proctor and Josh Meekings also started for Caley Thistle, while Thomas Piermayr, Ross Tokely, Graeme Shinnie and Billy McKay were substitutes.
Roman Golobart and midweek substitute Andrew Shinnie missed out completely after suffering injuries which will see them sidelined long term and Lee Cox missed out due to a calf problem.
Hearts made one change to the team who beat St Mirren 5-2 last Saturday with suspended Marius Zaliukas replaced by Ryan McGowan.
In blustery conditions the visitors started brightest with Hamill's 35-yard strike hammering the crossbar after just four minutes.
The hosts responded with a Greg Tansey free-kick which was comfortably saved by Marian Kello.
The Slovakian was in action again when he saved low from Inverness captain Richie Foran and moments later the Irishman fired wide.
Gregory Tade was next to force a save from the stopper after connecting with a Tansey cross.
Substitute David Templeton produced the Edinburgh club's first shot on target when his 25-yard curler was saved by Esson.
Inverness continued to dominate possession but Hearts absorbed the pressure as chances were limited.
Gillet had a goal ruled out for offside in the 36th minute after good work from Hayes, whose shot rebound off Kello to Sutherland and then the keeper again to the Frenchmen.
Ross was next to threaten when his 25-yard effort evaded Kello but drifted inches wide before Tade steered an effort wide in stoppage time.
The host's stayed on top after the interval and finally made their pressure count when Sutherland netted his first goal of the season.
The 21-year-old connected with a Hayes cross to power home a header which hit Kello before crossing the line.
Hearts rallied and former Inverness midfielder Ian Black tested Esson with a long-range free-kick.
Sutherland's cross-shot almost caught out Kello as it rebounded off the past.
Hearts substitute Suso Santana tried his luck with the wind behind him but the angled shot from distance was just off target.
Kello denied Hayes when Caley Thistle might have doubled their lead going into the last 10 minutes.
The Irishman was played through on goal by Tansey with only the goalkeeper to beat but squandered the chance.
Rudi Skacel's shot went inches over as Hearts searched for a leveller.
Hearts might have had a penalty with five minutes to go when Meekings felled Templeton but referee Salmond was not convinced.
John Sutton sent a low shot wide in the closing stages but Inverness held on for the victory and remain undefeated in 2012.
