Ugandan striker Villa Orochum scored the lone goal to help his team claim maximum points against their hosts.
The Mailmen came into the match hoping to get maximum points against the Kisumu-based side to take their tally of the season to seven points after managing to get four from their initial two games.
Stima had drawn 2-2 and 0-0 with Kariobangi Sharks and Wazito FC, respectively, and a win was much needed on Sunday to boost the players' confidence.
The Babu Salim-led side sat back and relied on counter-attacks and the tactic paid dividends on the half-hour mark, when they won the ball deep in their half and Oromchan ended it with a one-time finish, giving Jairus Adira no chance.
Rangers could have equalised with about 10 minutes to go when the hard-working Mbugua Simon danced his way past the defenders before cutting the ball back to Brian Osumba, whose shot went agonisingly wide.
On the other end, Henry Onyango went for power instead of precision and wasted a golden chance for Stima to double the advantage when put clear by Oromchan.
Stima are unbeaten in the three games and have collected five points in the process while Rangers have collected four from the same number of games.