The Swiss second seed, who owns four titles at Melbourne park, beat Australian Bernard Tomic 6-4, 7-6 (7-5), 6-1.
Raonic, seeded 13th from Thornhill, Ont. lost to Federer three times in 2012.
"I've had my three shots against him, and I look forward to my fourth," said a confident Raonic."
"Against Roger, one thing that has sort of worked well for me, I try as much as I can not to play on Roger's terms, to play on my own terms," he added.
Raonic struggled initially in the 50-minute opening set as he faced the 19th-ranked Kohlschreiber for the first time.
But he quickly got a grip on the match and went on to dismiss Kohlschreiber in one hour, 52 minutes, firing 44 winners, including 23 aces, and making 38 unforced errors.
It's the third time Raonic has entered the second week of a major. He made it to the final 16 at the US Open four months ago and got to the fourth round in Melbourne in 2011.
"A lot of good things are sort of coming together,"said Raonic of his improving game. "I'm just getting better and better. I'm struggling with a few things. But day-in, day-out, it's better."
The 22-year-old also revealed that he's been ill this week. "I just struggled with a fever the last two nights," he said.
He said his body ached during the match but he didn't really feel like he was struggling with energy. "I'm just happy how I put it aside and how I played," he said.
Meanwhile doubles veteran Daniel Nestor, of Toronto, reached the third round with new partner Mahesh Bhupathi.
The fifth seeds beat Romanian Victor Hanescu and Martin Klizak of Slovakia 6-1, 7-6(8) to set up a meeting with Italians Simone Boelli and Fabio Fognini.
The victory took just under 90 minutes, as Nestor and Bhupathi served up five aces and broke serve twice.