The striker scored deep into stoppage-time at Tulloch Caledonian Stadium to secure victory, leaving Thistle at the bottom of the SPL as the only team with no points.
Caley Thistle's Gregory Tade and Hibs' Ian Murray both had goals ruled out for offside, while Greg Tansey hit the post late on for the hosts when both sides searched for the winner.
Colin Calderwood's men looked to improve on back-to-back 2-0 defeats at Blackpool midweek and at home to Celtic last Sunday.
New signing Junior Agogo missed out, as did Sean O'Hanlon (broken toe) - who was replaced by David Stephens.
But Scotland Under-21 internationalists Callum Booth, Paul Hanlon and David Wotherspoon were on show for the visitors.
The home side's Nick Ross was also named in Billy Stark's squad for the friendly against Norway at St Mirren Park on August 10 and lined up alongside new signings Owain Tudur Jones and Thomas Piermayr. Andrew Shinnie and David Proctor missed out as Inverness sought to bounce back from the 3-0 loss at Motherwell last week.
Ivan Sproule bundled his way past a couple of challenges only to be thwarted by a terrific tackle from Inverness defender Kenny Gillet as the visitors carved the first opening. The French full-back threw himself in front of the early goalbound effort.
Inverness might have been given a penalty when Gregory Tade appeared to have been felled by Hibs' captain Ian Murray, but referee Steve Conroy was not interested.
Goalkeeper Ryan Esson was on hand to stop O'Connor's powerful strike after he connected with a Lewis Stevenson cross.
Butcher left his seat in the stand to shout encouragement from the touchline seconds before Esson stopped another O'Connor effort, this time using his face. The striker was played in by Murray but failed to find the net from around six yards.
Home captain Richie Foran should have done better on the half-hour mark when he was found in space with a flicked header from Tom Aldred after a Jonny Hayes cross. The Irish attacker blazed his volley over the bar in the Inverness' first clear-cut chance.
Three minutes before the interval Tade headed over from close range after a Hayes cross.
Seconds later Tade found the net after a cut back from Foran but it was ruled out for offside.
After the interval, Stevenson might have opened the scoring out of nothing when he tried his luck from 35 yards. The ball broke to the midfielder who fired his effort inches wide of the top corner of the goal.
Murray found the net from close range just after the hour following a Wotherspoon cross but it was ruled out for offside.
Caley Thistle responded swiftly with substitute Aaron Doran aiming a cross towards Foran but Victor Palsson nipped in to clear.
Sproule broke forward seconds later and his cross led to a volley from Matt Thornhill which was acrobatically turned over by Esson.
Caley Thistle substitute Shane Sutherland fired over with 15 minutes to go after being found by Foran.
Aldred steered a low Hayes cross wide before Jones found Sutherland, who forced a save from Hibs' goalkeeper Graham Stack as Inverness searched for the opener.
Foran seemed to be felled in the closing stages by Paul Hanlon but Conroy waved away the penalty shouts from the home fans.
With a minute remaining Tansey fired against the woodwork after a Hayes corner.
O'Connor ensured Highland heartache when he netted the winner with practically the last kick of the match, with his angled 12-yard effort beating Esson.