The Belgian struggled to get to grips with left-hander Koehler's serve in the first set but gradually moved up through the gears to run out a 7-5 6-1 winner.
Clijsters, who beat Li Na in last year's final at Melbourne Park, said it was a good feeling to step out onto Rod Laver Arena again.
"It's great to be back, I always love coming to Australia but the feeling is even stronger after last year," said the 11th-seeded Clijsters. "It's great to be back on this court as well, it brings back a lot of good memories.
"But I was focused out there because I was playing a good player. I had to be on my game from the start today."
Koehler, who beat American Julia Boserup to make the main draw, came out blazing and had Clijsters on the back foot for much of the early exchanges.
However, after double faulting to lose the first set, Koehler's serve deserted her in the second and Clijsters had no trouble closing out the match.
The 28-year-old, who could meet China's Li in the fourth round, said she had completely recovered from the hip injury that had forced her to pull out of the Brisbane International earlier this month.
"Your body has to get used to it," she said. "It doesn't matter how hard you train in the offseason, matches put so much more strain on your body because of the emotions and the pressure and the stress involved."