Two further tries followed in the opening stanza, scored by mobile lock Mitch Holten, with St Peter's getting one back after Tauranga foolishly ran the ball out from behind their goal line and lost possession.
Tauranga scored shortly after the second half restart when prop Sam Veikoso crashed over under the posts to make it 22-7. Fullback Harris Williams benefited from some straight line running by captain Brad Armstrong to score unopposed, and replacement prop Afa Popalli'i finished off with the final try.
Tauranga coach Jason Spice was pleased to see his players notch their first win of the season after some tough games, including their last start against Hamilton Boys' High School.
"We have been working on new things that we have been getting closer each week to pulling off," Spice said. "Today we scored a few tries out of them. Without scoring points there is always self doubt so it will be good for confidence.
"There is lots of tough stuff to come (Super 8). We are down on numbers and we just regroup every week. It has been a funny old start to the season. We took lots out of the Hamilton Boys' game. They scored three tries in the last 10 minutes but up until then we were right in the game."