Don Cowie gave the home side the lead when he raced on to a Ian Black pass before finding the net with a deflected finish.
But Colin Nish netted Hibs' first ever goal in Inverness immediately after the restart when he beat the offside trap.
Former Stoke striker Adam Rooney made his first start for Inverness as he replaced Russell Duncan, who missed out with a hamstring injury.
Hibs midfielder John Rankin returned to face his former club as visiting manager Mixu Paatelainen named the same team that started in last week's 3-2 home victory over Falkirk.
Newest recruit Steven Pinau, on loan from Genoa, began on the bench for the visitors.
The home side took the game to the visitors with the Caley strike force of Andrew Barrowman and Adam Rooney looking very lively in the opening period.
Inverness almost went ahead in the third minute when Dougie Imrie played a free-kick short to Ian Black whose cross found Rooney.
The former Stoke player's header in turn found the advancing Ross Tokely but the Caley stand-in skipper's header was brilliantly pushed over the bar by Andrew McNeil in the Hibs goal.
Steven Fletcher looked to have picked up an injury when he came off second best in a challenge with Jamie Duff.
And while the Hibs forward was on the floor, injured Caley created a good opportunity, with Rooney latching on to a Hastings cross but the forward's attempt fell easily into the hands of McNeil.
John Rankin had a great chance to get on the scoresheet against his former club when he raced on to a Fletcher pass but the midfielder dragged his shot wide.
The home side took a deserved lead in the 21st minute when Ian Black played a tremendous ball over the top which Cowie raced on to and cut inside before firing a deflected shot past McNeil with his left foot.
Nish had a great chance to level the scores after 28 minutes when he found himself one-on-one with Michael Fraser - but the big striker showed a lack of composure by volleying over the bar from the edge of the box.
Hibs had a big shout for a penalty turned down three minutes later when Dean Shiels looked to have been bundled over in the box by Richard Hastings when he was quickest to react to Fraser spilling Fletcher's shot - but referee Eddie Smith waved away the visitors' protests.
Fletcher should have done better when he met Alan O'Brien's cross on the turn in the penalty area but the striker's volley was straight at Fraser.
On the stroke of half-time, Rooney had a chance to double Caley's lead following a scramble in the box from an Imrie corner but the Irishman's effort was cleared off the line by Nish.
Craig Brewster would have been furious as his side allowed Hibs to get back on level terms within a minute of the re-start.
A Dean Shiels shot fell kindly into the path of Nish, and while the Inverness defence were claiming for offside, the big striker slid the ball past Fraser.
With the home side looking rattled, Hibs could have edged ahead when Fletcher sprayed a beautiful diagonal ball to O'Brien and his left-foot cross found Nish, whose header hit the post and bounced away to safety.
Lionel Djebi-Zadi was given his Caley debut when he came on for Imrie 11 minutes into the second half.
And Caley almost restored their advantage when Barrowman nodded a McBain corner into the path of McGuire but McNeil was equal to the defender's attempt.
Both teams freshened things up after 65 minutes with Iain Vigurs coming on for McBain and Hibs bringing Filipe Morais on for O'Brien.
With less than fifteen minutes remaining, Hibs could have taken the initiative when a Hanlon cross found Nish, who fed in Morais.
But the substitute's woeful effort sliced away to safety.
Brewster brought on Barry Wilson, who celebrated his testimonial midweek against a Liverpool XI, for Barrowman, while Lewis Stevenson came on for Hibs in place of the tiring Hanlon with 10 minutes to go.
In the 82nd minute, Dean Shiels spurned a glorious chance when he was played in by Nish but the midfielder could not find the target.
Black was booked for tripping Morais after a wasted free-kick in a promising position by Wilson.
Hibs introduced new signing Steven Pinau for Joe Keenan in the closing stages and the Frenchman could have won the game but he lashed the ball over the bar.
There was still time for Hastings to be booked for a crude challenge on Fletcher and Black to shoot wide.