Debutant Barrowman latched on to Ross Tokely's 27th-minute cross to give Craig Brewster's men the ideal start on Saturday.
And McBain scored late on to give Caley Thistle their first competitive win over the Dons.
Charlie Mulgrew, Mark Kerr and Gary McDonald all made their Pittodrie bows in the Aberdeen starting XI.
Brewster handed Barrowman, a summer recruit from Ross County, a start up front for Caley Thistle while other new boys Ryan Esson and French defender Lionel Djebi-Zadi had to be content with places on the bench.
Aberdeen exploded out of the traps and enjoyed the better of the opening exchanges. A clever volley across the face of goal from Kerr almost allowed Lee Miller to open his account in the first minute but the cross was just in front of the striker.
Minutes later Chris Maguire raced onto a Miller header but the young striker lacked composure and volleyed wide from the edge of the box.
When Inverness, playing with just Barrowman up front, did make it into the Dons half they struggled to trouble Jamie Langfield in the Aberdeen goal.
Barrowman raced onto Tokely's ball over the top but the 23-year-old's cross found no takers.
The breakthrough came in the 27th minute and it was the visitors who went ahead against the run of play after Kerr was caught in possession by Russell Duncan in the middle of the park.
Caley worked the ball out to Tokely on the right and his driven cross along the face of goal gave new boy Barrowman the easiest of finishes.
Aberdeen had a chance to get back level after Jeffrey De Visscher was tripped by Don Cowie on the edge of the area but Mulgrew blasted into the Caley wall.
Darren Mackie came on for De Visscher at half-time as Aberdeen looked to get back on level terms.
However, it was Inverness who almost increased their advantage when Dougie Imrie cut inside and fired a left-footed shot just past Langfield's post.
A corner by Mulgrew was headed behind under pressure by Maguire as Aberdeen regained the initiative.
The following corner was met by a speculative overhead kick from substitute Mackie, which fell weakly into the arms of Michael Fraser.
Dons boss Jimmy Calderwood brought on Derek Young for Maguire after 64 minutes as Aberdeen looked for an equaliser but it was Imrie again who could have doubled Caley's advantage when he raced on to a flat Langfield kick-out but his shot was too high.
Andrew Considine was booked for bringing down Duncan but Tokely's free-kick came to nothing and, with a quarter of an hour remaining, the Dons replaced Kerr with Zander Diamond.
Ian Black's long-range shot flew over the bar before he was replaced by Barry Wilson, then Tokely was booked after a foul on Young.
And the Dons were doomed when Imrie set up McBain and he finished from inside the area. Jamie Smith hit the post at the home side tried to salvage something but Miller was booked for dissent as Inverness held on.