Kilmarnock players were incensed as Barrowman was awarded a penalty
Inverness moved up to fourth in the league with a convincing win over Kilmarnock at home.
Connor Sammon put the visitors in the lead on four minutes with a tap-in from close range.
Inverness drew level on 21 minutes from a Phil McGuire lob over Alan Combe, before Andy Barrowman scored a penalty two minutes before half-time.
And Inverness sealed the victory in the 81st minute when Ian Black rose to head home a corner from Iain Vigurs.
The game was only four minutes old when Inverness gifted their visitors an early lead.
Michael Fraser left his goal unguarded when he came out to gather a Jamie Hamill free-kick.
The ball fell to Simon Ford whose shot deflected kindly into the path of Conor Sammon who had the easiest of finishes.
The home side could have got back on level terms in the 14th minute but Roy McBain failed to find the target with an ambitious lob after good work by Dougie Imrie and Barrowman.
And Kilmarnock goalkeeper Alan Combe was rescued by Sammon when he headed Barrowman's effort off the line.
The home side got back level in the 21st minute when Kilmarnock failed to deal with an Imrie free-kick and the ball dropped to Phil McGuire who gave Combe no chance with a left-foot lob.
And they took a half-time lead thanks to a controversial penalty from Barrowman, who was accused of diving to win the spot-kick.
Kilmarnock's day got worse when they were reduced to 10 men in the closing stages, with Jamie Fowler given a second booking for handball.
And Inverness then sealed their victory in the 81st minute when Ian Black rose to head home a corner from Iain Vigurs and the best efforts of David Fernandez could not stop the ball creeping under the bar.
Adam Rooney could have added a fourth for Caley Thistle just before the end but the Irishman headed wide.
But that was immaterial as the Highlanders secured their first home victory of the season.
Inverness manager Craig Brewster: "That's out first home win and it sets us up nicely. I was just please at an all-round great team performance.
"Kilmarnock had a great chance to make it 2-0, but credit to the players who kept their calm when everyone else in the stadium was getting nervous.
"We got the equaliser at the right time and we gained confidence, even when we lost the early goal we knew there was still over 80 minutes to go.
"And once we started moving the ball around they couldn't live with us.
"Andy Barrowman's penalty was a game-turning moment. I didn't see it well as I was 80 yards away.
Kilmarnock manager Jim Jefferies: "We started the game well and Conor Sammon missed a glorious chance to double our lead.
"Then their goal gave them a lift and we stopped playing. The second half was abysmal from us - it wasn't a Kilmarnock performance.
"The boys were all complaining about the penalty - which I haven't seen. But then Fowler got booked complaining, which cost us later in the game when he was sent off.
"It was night and day compared to the Aberdeen match in mid-week. Maybe they thought today was going to be a doddle and Inverness showed them it wasn't.
"None of my team out there today got any pass marks at all."
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