Brook, who won the belt from Shawn Porter in August, remained unbeaten after his 23rd knockout win in 34 fights.
Only six months ago, the British boxer was attacked on holiday in Tenerife, stabbed in the thigh with a machete by an assailant yet to be caught. He needed 60 stitches.
"I never thought I'd walk again, let alone box, and here I am filling arenas," Brook told the crowd. "I can't put in words how much it means to me to come back and defend my world title."
Dan, a Romanian based in Montreal, might need stitches, too, after he was put down twice in the second round and twice more in the fourth.
The first time in the second round, a right uppercut put Dan on one knee, then a right cross from Brook earned Dan a second standing eight count. Dan endured the third round, but Brook found his range again in the fourth.
A right-left combo with an uppercut caused Dan to lose his legs, then right on the bell, Dan threw a wild right and Brook caught him unbalanced with a left hook. Dan did a roll on the canvas, and had to be directed to his corner, where his trainers told referee Earl Brown to end the fight. Dan's record dropped to 34-3 (18 KO).
"He showed heart," Brook said. "I hit him with some good, clean shots, and he kept getting back up. I knocked the cobwebs off."
Brook said he has a ringside ticket to watch the megafight between fellow welterweights Floyd Mayweather and Manny Pacquiao in May in Las Vegas, and hopes to eventually fight the winner.