It was by no means a classic performance from the 33-year-old Leeds fighter but she did what was needed to set up a semi-final with China's Ren Cancan, the woman she beat in the London 2012 final.
Cancan, who beat Adams in the 2010 and 2012 world championships finals, saw off Canada's Mandy Bujold by the same 3-0 scoreline.
"I felt a little bit rusty, I haven't boxed since the world championships," Adams, the first woman to win an Olympic gold in boxing, told reporters.
"But I can build from that one now. I've got the win out of the way, pressure's off a little bit, I've sealed a medal and now it's just a chance to change the colour."
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Adams won the world championship title, her first, in Astana in May. She had previously won three silvers.
Victory in Rio would make her the first Briton to win two Olympic titles since London policeman Harry Mallin won middleweight gold in 1920 and 1924.
Adams won the first round 10-9 on all three scorecards but lost some momentum in the second as she toyed with Kob's defence.
"The tactics were at first to move around her...I wanted to see what she was like going back so the next two rounds I decided to go forward a little bit, play her at her own game," she said.
Ireland's Katie Taylor, the 2012 lightweight champion, lost her opening bout on Monday but Adams said that upset was not on her mind.
"I just have to focus on what I'm doing in the ring," she said. "If I start thinking about all that I'll lose my focus and be concentrating on other things than just getting in there and trying to win."
(Reporting by Alan Baldwin, editing by Clare Lovell)
