Gary McDonald's header from a Charlie Mulgrew free-kick after 79 minutes was enough to separate the sides in a disappointing contest where goalmouth action was at a premium.
However, the win was just the result Aberdeen boss Jimmy Calderwood would have been looking for with a section of the Red Army set to stage a protest against the current management regime after the game.
Aberdeen made one enforced change to the side that drew 1-1 with Motherwell with winger Sone Aluko returning in place of the suspended Andrew Considine.
The visitors, who were out to match their opening day success at Pittodrie when they defeated the Dons 2-0, also made one change.
Ryan Esson returned from suspension to take his place in goal for the visitors with Michael Fraser dropping to the bench.
The game kicked off following a minute's silence in tribute to the 16 men who lost their lives in the recent helicopter tragedy in the North Sea.
The visitors started brightly and slack play from Jamie Smith and Lee Mair gave David Proctor an opening but the Caley midfielder's shot from distance was charged down by Charlie Mulgrew.
Filipe Morais, in confident mood following his brace against St Mirren last week, tested Jamie Langfield with a couple of early efforts but the Dons goalkeeper made comfortable saves on both occasions.
Despite Caley's early dominance it was the home side who should have taken the lead when an accurate Derek Young cross found Lee Miller but his header was magnificently saved by Esson.
A powerful free-kick from Mulgrew was deflected over the bar and Lee Mair headed wide from the resulting corner as the Dons began to settle into the game.
Miller was then inches away from connecting with an Aluko cross after 27 minutes as the Dons continued to press for an opener.
Selfish play from Morais then prevented Inverness taking the lead with five minutes to go until half-time.
The Portuguese attacker exploded past Mulgrew but opted to shoot for goal himself from a narrow angle instead of passing to one of his better-placed team-mates and Langfield made an easy save.
Inverness started the second half in a positive fashion with Morais shooting over the bar before smashing a free-kick into the wall in the opening minutes.
But it was Aberdeen who were cursing their luck at the other end after 56 minutes when Esson fumbled a hanging Mulgrew cross but McDonald's shot on the rebound was deflected wide.
And minutes later everyone inside Pittodrie was at a loss to explain how Chris Maguire failed to open the scoring when the ball fell kindly into his path after Aluko had stung the palms of Esson but the young striker's effort came back off the crossbar.
Aberdeen were now in the ascendancy and Maguire was appealing for a penalty when he fell in the box under pressure from Lionel Djebi-Zadi but the referee waved play on.
Inverness made their first change of the day with Russell Duncan replacing Ian Black after 65 minutes.
Andy Barrowman came on for the tiring Morais soon after as Caley tried to survive the constant Aberdeen pressure.
A Smith corner fell to Aluko on the edge of the box but the young Englishman's right-foot shot was well handled by Esson.
Aberdeen finally took a deserved lead after 79 minutes when McDonald headed home a Mulgrew free-kick, much to the relief of the home support.
The Dons could have doubled the lead three minutes later but Esson made a fine stop from Lee Mair's low drive and Miller could not convert the rebound.
Aberdeen, looking to see out the last five minutes, made a double substitution with Tommy Wright and Darren Mackie coming on for Miller and Maguire.
The home side survived a late spell of pressure from Terry Butcher's side to earn three crucial points.