The London super-middleweight signed for Matchroom Sport on Monday and immediately stepped into the ring with his new promoter, extending his unbeaten career to 17 fights in the process.
He had Balmaceda down on his knees after some good work to the body in the second and then finished him off with a straight right to the head 50 seconds into the third.
Balmaceda spat his gumshield out and remained on one knee for the count, giving Groves a routine victory.
"I've had to put distractions to one side, come out and be on form," Groves told Sky Sports 2.
Promoter Eddie Hearn was keen to push Groves forward as well, adding: "He's ready for a big fight now."
Darren Barker then breezed past Italy's Simone Ritolo in similarly convincing fashion to claim the vacant IBF Inter-Continental middleweight title.
A straight right late in the fourth rocked Ritolo back on to the ropes and, after referee Steve Gray spoke with Ritolo's corner between rounds, the fight was called to a halt with a hand injury to the Italian cited as the reason.
It was Barker's 25th win in 26 fights, and his second in three months, and he told Sky Sports 2: "I'm ready to push on now.
"There's the obvious domestic fights and world title fights - I'm game, I'll fight any of them. It just takes two of us to get the ball rolling and it could be rematches, trilogies, whatever."