The Scottish champions, who lost four friendly encounters during a summer tour of Germany and Austria, travelled south to London on the back of Wednesday night's three-goal win over Cliftonville in their Champions League second-qualifying round first leg.
But despite fielding a side that included only skipper Efe Ambrose from the win at the Northern Irish side's Solitude home, Neil Lennon's youthful team was too strong for Uwe Rosler's men at Griffin Park.
Amido Balde and McGregor were on target for the Hoops after Adam Forshaw had given the hosts an early advantage.
Cheered on by a 6,000-strong away support, Celtic handed starts to Tom Rogic, Dylan McGeouch and Tony Watt after all three made substitute appearances in their European clash.
Australian international Rogic was first to threaten with a shot over Jack Bonham's crossbar in the first minute, but Brentford were soon ahead.
Martin Fillo beat both Ambrose and new Bhoys defender Steven Mouyokolo before clipping a cross to the back post which Forshaw nodded past Lukasz Zaluska in the visitors' goal after 10 minutes.
But Portuguese frontman Balde got his first goal in Celtic colours 13 minutes later when he collected a pass from Watt and used his strength to hold off a couple of defenders before bundling his finish past Bonham.
Balde and Watt both hit the bar in the moments before the break, but Brentford's luck ran out as the Hoops countered swiftly in the 57th minute before working the ball to 20-year-old McGregor who swept home a fine finish into the bottom corner.