The Serbian, who is eyeing a 22nd major to match Rafael Nadal, looked uncertain in his movement in a roller-coaster opening set where he began with a break, squandered three set points at 5-3 and dropped serve late on before edging a thrilling tiebreak.
A heavily-strapped but more aggressive Djokovic emerged from a medical timeout and built pressure with his relentless returns from the back, going up 4-2 as 27th seed Dimitrov hit the net to surrender his serve, and went on to wrap up the second set.
A half-fit Djokovic can still be a handful for most players but the fourth seed looked a little more certain of his mobility in the third set and a double break to start helped him subdue the error-prone Dimitrov who failed to make a late comeback.