Tries from flanker Arno Botha as well as wingers Lionel Mapoe and Akona Ndungane combined with 13 points from Morne Steyn's boot moved the three-times champions to the top of the South African conference.
"It was a great team effort, it's not easy to come here and win," Bulls skipper Pierre Spies said in a pitchside interview. "In the second half we felt we just had to be clinical and that's what it was, a clinical performance."
Kirwan, who opened his reign as Blues coach with shock wins over the Hurricanes and Crusaders, fielded six debutants in a gamble which proved too great for his fledgling enterprise.
A try from Rene Ranger four minutes from time added to Charles Piutau's 52nd minute effort to offer the home side hope, but it was too little to make up for a lacklustre first half display.
"We just didn't turn up in the first half, I'm gutted ... we'd earned some respect and then we lost it," said a clearly fuming Blues skipper Ali Williams.
The Bulls, who had also won their first two matches of the season, led 15-6 at halftime after Mapoe and Ndungane had run in tries on overlaps caused by unrelenting pressure on the home defence.
When Piutau crossed and Baden Kerr converted seven minutes into the second half, however, the crowd were roused and the Blues took a slender one-point lead.
It only lasted four minutes, however, as the South Africans swung their attack back and forth across the park through multiple phases before Botha was able to run around the defence and touch down with a man free outside him.
Blues replacement Angus Ta'avao dropped the ball with the line at his mercy seven minutes later and it was not until centre Ranger sprinted down the right touchline and bulldozed over the last defender that they were able to add a second try.
Any hopes they had of rescuing the match died when lock Liaki Moli ran the ball into touch from the kickoff, however, and Steyn added his third penalty with the last kick of the game.