The quarterback had come under fire following back-to-back losses for last year's NFC champions, having thrown four interceptions and been sacked six times during the defeats.
The team's head coach told reporters: "Kap was seeing the field and delivering the ball. He played with great poise. He was really locked in and focused all week."
Kaepernick added: "We knew we had to win. It's a big win for us. It's a divisional win."
The 25-year-old made 167 passing yards, two touchdown passes and was sacked just twice during the 35-11 win.