Aguiar missed one of several chances in a thrilling finale at Easter Road on Sunday to leave just a point between the sides in the top half of the Scottish Premier League.
Aguiar had been sidelined by ankle and knee problems since April 2007 and was one of four players drafted in by Csaba Laszlo.
Christian Nade started for the first time this season after Mike Tullberg suffered another injury, while Andrew Driver returned from injury and Eggert Jonsson came back from suspension. Hibernian had gone above Hearts after completing their third win in four games, the exact opposite of the Gorgie club's recent form, and their front three quickly opened up the Hearts defence.
Colin Nish ran on to Derek Riordan's clever backheel and squared for Fletcher to force home from close range.
Hearts came close to an instant reply when Christophe Berra headed against the bar after Laryea Kingston had lobbed the ball in after his half-cleared corner.
The action was coming thick and fast and Riordan volleyed into the side net after David van Zanten's cross found him unmarked at the back post.
Kingston missed a great chance in the 11th minute after starting a counter-attack following Steven Thicot's misplaced pass. The Ghana midfielder played Nade through and the ball fell for him on the right side of the box after Yves Ma-Kalambay had come out to slide clear, but he shot high and wide.
Riordan came close from a 45-yard free-kick, which had Marian Kello moving quickly to guard his top corner.
Kingston again played Nade in with a lofted ball but the striker got his attempted volley all wrong.
Riordan claimed strongly for a penalty when he was felled by Jonsson after Kello's latest poor clearance, but Eddie Smith waved play on.
The match entered a scrappy phase, not helped by lengthy treatment for Kello after he was caught by Nish in the air.
Aguiar sliced a half chance well over from 16 yards, but the Portuguese midfielder made amends in the 42nd minute when he curled into the bottom corner after Nish had pushed over Lee Wallace.
Both goalkeepers threatened to gift goals before the break, first when Ma-Kalambay spilled Nade's ambitious 30-yard drive. Dean Shiels mis-hit from 15 yards as he and Nish ran on to Fletcher's clever lay-off and Kello then let a backpass run under his foot before sweeping the ball away.
Hibs threatened first in the second half when Janos Balogh, who came on for Kello at the break, scrambled to push Riordan's lopping header wide of his near post following van Zanten's deep cross.
Nade nodded home Kingston's corner on the line moments later but he had impeded Ma-Kalambay and Smith blew for a foul.
Aguiar was becoming increasingly influential and Nade soon headed wide from another Kingston cross.
Hearts continued to push forward but Fletcher shot into the side net at the other end after a long throw.
Hibs were grateful to Lewis Stevenson for blocking Kingston's shot with Ma-Kalambay out of his goal after pushing wide Driver's deflected effort.
Riordan won a free-kick from Jonsson in almost exactly the same position that Aguiar scored from, but Balogh got down well to hold the former Celtic player's effort.
Ma-Kalambay punched clear as Kingston again aimed a corner towards Nade on the line as Hearts continued to edge possession.
The home fans were growing frustrated but Riordan had them off their seats when he volleyed towards the top corner after van Zanten's crossfield ball. However, Balogh leapt to push the ball wide.
Mixu Paatelainen gambled in the 80th minute by replacing holding midfielder Thicot with the attack-minded Fabian Yantorno.
It nearly paid when Nish headed Riordan's cross into the path of Fletcher, but the Scotland striker volleyed just over from 16 yards.
Balogh then spilled a Riordan cross but the ball fell kindly into his path. His clearance led to Aguiar missing the chance to become an even bigger hero as he fluffed his left-foot shot from 12 yards after Driver's cutback found him unmarked.
The game was finishing as dramatically as it started and Balogh came to the rescue as he grasped the ball from Riordan's feet after the Hibs forward was put clean through by a weak backpass from Marius Zaliukas.
Nade then skied over from 10 yards in injury-time after another cutback from Driver.