The Ospreys clinched a crucial win in dramatic fashion, Sam Davies kicking the winning conversion in the 80th minute following Ifan Phillips' late try at the Liberty Stadium.
After a sluggish start that saw the visitors race into a 12-point lead early on, the Ospreys regrouped at half-time and showed great character to claim the victory.
There were also tries for Ashley Beck and Sam Cross, while Davies kicked 12 points as the Ospreys kept their Champions Cup qualification hopes alive with their second win against South African opposition in as many weeks.
They led for just 20 seconds in total but nobody at the Liberty Stadium was worried about that as the final score was all that mattered.
The Ospreys were slow out of the blocks as Cheetahs enjoyed the better of the opening exchanges, a clearance out on the full from Reuben Morgan-Williams giving them field position to build from.
Twice they went to the corner, only for Nico Lee to be held up as tried to barge his way over the line from close range.
The visitors were able to keep up the pressure and it looked like a score for Reniel Hugo as it opened up for him but the big second row lost the ball forward as he reached for the line.
It was one-way traffic and, in the 10th minute, some good work by Francois Venter almost created the opening try, a combination of Malcolm Jaer and Lee held up.
The score had to come and it did less than 60 seconds later, the Cheetahs opting to keep it tight at the lineout and driving their way over from close range for Torsten van Jaarsveld to score, the try going unconverted.
The pressure from the home team was relentless, the Ospreys unable to get any possession or territory in the opening 15 minutes and it came as no surprise when the Cheetahs extended their lead. Backs and forwards combined to give Hugo the simplest of finishes under the posts, brushing off some ineffectual tackling to score, Niel Marais converting.
Having waited until almost 20 minutes to get inside the opposition 22, a good scrum provided the Ospreys with their first opportunity, first Tom Habberfied and then Morgan-Williams going close.
With a penalty on the line, they opted for a scrum, applying pressure that saw Cheetahs penalised three times at the setpiece. At the fourth attempt, the Ospreys couldn’t get the drive on so looked to play it, Kieron Fonotia and then James King carrying well before Dmitri Arhip was penalised for holding on.
Despite not troubling the scorers, the Ospreys were starting to enjoy more of the game, but it was the visitors who were next to threaten, Craig Barry running a good line only to be halted five metres out four minutes from the break, the home team winning the scrum to clear.
With time up in the first half a good break from deep saw the ball worked wide to the right where Guy Mercer freed Jeff Hassler to carry 50m upfield to the Cheetahs 22. Hands in the ruck saw the Ospreys awarded a penalty, Sam Davies slotting over the kick to send his team down the tunnel trailing by nine.
HALF-TIME: OSPREYS 3-12 TOYOTA CHEETAHS
With a half-time talk from Allen Clarke obviously ringing in their ears, the Ospreys began the second half with increased urgency and were rewarded with, their first try inside three minutes, good pressure and positive intent eventually seeing Beck winning the ball in contact before showing great strength to power his way over. Davies’ conversion meant the deficit was now just two points.
Cheetahs hit back almost instantly through a length of the field score, the Ospreys coughing up possession in the opposition 22 which allowed their opponents to launch a stunning counter. Hassler was caught between going for the ball carrier and the man on the overlap and the outside pass allowed Lee to carry almost 80m for the score, converted by Marais and the scoreboard now read 10-19.
Despite that setback the Ospreys were looking livelier and try number two arrived in the 55th minute after patient build-up play. Good work from Mercer, Beck and Dan Evans, eventually saw Cross collecting the ball at speed and there was no stopping him at close range as he scored his third try in five games for the Ospreys, his first in the PRO14, before Davies added the extras.
The Ospreys were their own worst enemy once again just two minutes later, on the attack and looking dangerous only for Hassler’s telegraphed pass in midfield to be picked off with ease by Barry, the winger racing clear to score the bonus point try from 60m, converted by Marais.
The home team should really have scored their third when Davies broke the line before finding Evans, the fullback carrying to within five metres of the line before slipping it outside to Hassler. The Canadian had just grass in front of him but was unable to collect the ball cleanly, the ball going forward into touch allowing Cheetahs to clear.
The Ospreys were enjoying the better territory and possession now, despite the two lengthy run-ins that meant they were behind on the scoreboard, and they were back within a converted try with 11 minutes to play, Davies with the three after some exceptional rucking work from Mercer won the penalty.
Pressure was building and the Ospreys were looking likely to score next only for the ball to be lost close to the touchline deep inside Cheetahs territory. The visitors again countered quickly, Barry carrying well, and only good work from Mercer, forcing the ball forward in the pass, stopped a certain try for the South Africans.
That was to prove crucial as, with the clock ticking down, the Ospreys were able to get back upfield for one last opportunity and it was hooker Phillips, an early injury replacement for Sam Parry, who crashed over for the score to bring his team to within one point and just a minute to play.
It wasn’t a straight forward kick for Davies but he made no mistake to put his team ahead for the first time, with only 20 seconds left to play. The Ospreys had to withstand one last moment of pressure from the restart but they secured turnover ball allowing the outside half to put the ball out for a hard earned win full of character.