The Portuguese midfielder picked up an Andrew Driver pass on the edge of the box and twisted one way then the other before unleashing a low drive past Ryan Esson.
Inverness, who are still looking for a second home win of the season, dominated the second half but could not find an equaliser.
Adam Rooney and Andy Barrowman started for Caley after coming on as substitutes in midweek to help the Highlanders to a point against Falkirk.
Barry Wilson also made a rare start for Craig Brewster's side with Garry Wood and Iain Vigurs dropping to the bench, while Don Cowie did not make the squad because of a knee injury.
Hearts had the first opportunity in the opening minute when Munro was adjudged to have fouled Christian Nade on the edge of the box but Driver's free-kick sailed over.
The home side created a chance of their own a couple of minutes later following good work by Wilson. The midfielder got past two defenders before crossing for Barrowman who looked certain to score but his effort went wide.
Caley continued to push forward in the hope of drawing first blood with Ian Black finding Dougie Imrie but he rushed his effort and Janos Balogh gathered the ball easily.
Inverness boss Craig Brewster was forced to make an early change after 15 minutes with Roy McBain replacing Black who had earlier received treatment for a head knock.
Hearts were enjoying the bulk of the possession but the home side continued to probe forward on the counter and a clever first-time pass from Tokely released Wilson but he was foiled by a fine sliding tackle by Christophe Berra.
The visitors opened the scoring soon after. Driver found Aguiar in space at the edge of the box and the Portuguese midfielder made space before drilling a shot past Esson.
Nade skipped past two defenders on the edge of the Inverness before falling in the box under pressure from Munro but the Frenchman's appeals for a penalty were waved away by referee Mike Tumilty.
The home side were doing their utmost to get back in the game with Marius Zaliukas picking up the first booking of the day for pulling back McBain.
Barrowman was thwarted as the half drew to a close when he stabbed the ball past the onrushing Balogh but he and Rooney could not force the ball past the covering Hearts defenders.
There was still time for Rooney to be denied a penalty when he looked to have been pushed down by Wallace but referee Tumilty again waved away the protests.
Hearts could have doubled their lead within two minutes of the restart when Driver crossed for Nade but the Frenchman's powerful effort was blocked by team-mate Wallace.
The resulting corner, taken by Aguiar, fell to Driver on the edge of the box and his clever lob was tipped onto the bar and over by Esson.
Barrowman was replaced by Garry Wood soon after as the Highlanders looked to get back on level terms.
A long throw from Munro caused problems for the Hearts defence with Rooney having an overhead kick blocked before the ball eventually fell to Imrie on the edge of the box who could not keep his shot down.
The home side were dominating proceedings and Imrie was unlucky when he turned skilfully on the edge of the box before dragging his shot wide.
Neilson, who was making his first start for the Edinburgh side since April, tried to lob Esson after 78 minutes but the full-back's volley went wide.
Substitute Vigurs was denied by Balogh late on but Hearts held on for a third successive win.