Gutierrez, who has scored 10 goals in 177 league games since joining the club in 2008, was not used by caretaker manager John Carver but said it was an important step in his recovery.
"I'm really happy to be back," the 22-cap Argentina midfielder told the BBC. "It was my first time back since my illness. I'm strong and fit.
"After the illness, you need to get games. It's going to be tough. I'm going to fight for my place and when I have the opportunity I'll do my best."
Gutierrez has not played first-team football since a loan appearance for Norwich City last April.
"In football you never know what's going to happen," he added. "You start to think about life in a different way, things are more important than football.
"The chemotherapy was a big step, a big point in my life and I'm enjoying being back.
"I have to say thanks. The fans give me a lot of power to work through my illness. Not just Newcastle fans, but football fans. They sent me a lot of love and a lot of messages."
Victory was 11th-placed Newcastle's first in four games ahead of the visit of Manchester United to St James' Park on Wednesday.
(Reporting by Tom Hayward; editing by Ken Ferris)
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