The Warriors were slow out of the blocks in the second-half and Cowboys right wing Kyle Feldt scored twice, but two Johnson penalty goals kept them ahead with the Kiwi playmaker's late one-pointer clinching their sixth away win of the season.
"We were good in the first-half and scored some nice tries but obviously we were terrible in the second-half," said five-eighth Blake Green.
"We started slowly after the break and struggled to get out of our own end with a low share of the footy and used a lot of energy defending our own line.
"But we showed a lot of fight and resilience on our try line which was really pleasing."
Warriors centre Solomone Kata off was forced off with a hamstring injury early in the second-half, with next week's representative bye round expected to impact further on their roster.
Despite the ugly nature of the win, coach Stephen Kearney will be pleased his side got the job done ahead of a testing run of games in the next month against fellow top eight sides Cronulla (home), Penrith (away), Brisbane (away) and Melbourne (home).
"He was very happy," said Green.
"It's a really important win. To just keep racking up some points and be 10 out of 14, I'm wrapped with how we've played and we've put ourselves in a great position."
North Queensland opened the scoring with a penalty goal to captain Johnathan Thurston giving him 2100 career points, before the Warriors took control with Tuivasa-Sheck sparking a three-try blitz in his return following a week out with an ankle injury.
The Kiwi international provided the last pass for wing Maumalo and centre Kata to cross down the left edge and in between ran 75 metres and beat Cowboys fullback Michael Morgan to score his first career try against the Cowboys.
Bowen's try gave the home side belief and soon after the resumption Feldt crossed down a short-side before a Tuivasa-Sheck error saw Te Maire Martin break clear to send his wing in for his double.
Johnson's immaculate kicking proved the difference and consolidated the Warriors place in the top four ahead of their next game against the Sharks at Mt Smart Stadium on June 29.
Warriors 23 (Ken Maumalo, Roger Tuivasa-Sheck, Solomone Kata tries, Shaun Johnson 3/3 cons, 2/2 pens, 1 field goal)
Cowboys 16 (Javid Bowen, Kyle Feldt 2 tries, Johnathan Thurston 1/3 cons, 1 pen)