For the charging Force, it was their seventh win in 10 games and saw them settling in fifth position in the Super Rugby standings, tied on points with the fourth-placed Crusaders.
After going into the break trailing 16-6, Drotske said the message at half-time was to show more respect for the ball.
“We needed to protect the ball better, while we also conceded a lot of penalties at scrum time,” he said.
“The Force are excellent at the breakdowns and we needed to contest there, while it was vital for us to put phases together.”
The opening try of the game by Force fullback Jayden Hayward in the 25th minute came as a direct result of a Cheetahs turnover.
Former Cheetahs player Sias Ebersohn also converted all four attempts at goal for the tourists, while the home side’s Johan Goosen missed his first before bringing the Cheetahs back into the contest with two penalties.
The yellow card to Force captain Matt Hodgson opened the way for the Cheetahs to score their only try by No 8 Boom Prinsloo, reducing the deficit to 16-13 five minutes after the break, but then the Force stepped up.
The man nicknamed the “Honeybadger”, wing Nick Cummins, scored his sixth try of the season in the 53rd minute to again open up a 10-point lead at 23-13.
Crucially, Cheetahs prop Coenie Oosthuizen was denied a try 10 minutes from time when he was adjudged to have rolled the ball over the whitewash in order to win the decision.
It was the Force’s first win on South African soil since 2011 and their first over the Cheetahs since 2008.