But the Force missed out on a bonus point after Yamada crossed for his second try in the 79th minute.
Force skipper Matt Hodgson was disappointed with the late fadeout, but relieved to come away with a win.
"It wasn't the start we were after. But... I asked the team to be tough in those hard moments, and rebound from it," Hodgson said.
"I thought we did, and got momentum back our way for most of the first half.
"Obviously disappointed they crossed the line a couple of times (late). But I was rapt with our attack."
A rout of epic proportions appeared to be on the cards when Ben McCalman's try extended the gap to 33-5 early in the second half.
But the Sunwolves dominated the match from that point on, scoring three tries to one in the final 22 minutes to deny the visitors a bonus point.
The Force now have two wins to their name, and will be aiming to build on their latest result when they host the Blues in Perth next Saturday.
Meanwhile, the Waratahs secured three successive wins for the first time in 2016.
Bernard Foley on Saturday night marked his record-equalling 59th game as NSW five-eighth with a 16-point haul from a try, conversion and three penalty goals as the
Winger Reece Robinson collected NSW's other try, but the Tahs lamented being unable to clinch an all-important bonus point that would have sent the 2014 champions top of the Australian conference.
Robinson botched a golden opportunity in the 68th minute when he over-ran Kurtley Beale's pinpoint grubber kick into the Cheetahs' in-goal, while star centre Israel Folau crossed after the siren only for the try to be somewhat controversially disallowed.
Referee Nick Berry awarded the try to Folau before TMO George Ayoub overruled the on-field official after deeming Waratahs captain Michael Hooper had thrown a forward pass in the lead-up.
"Obviously it was disappointing at the end to miss out on that bonus point," Waratahs coach Daryl Gibson said.
"But we're very pleased to come away with a win in what was a pretty scrappy game for both teams, but a potential banana skin that we avoided."
With a game in hand over the conference-leading Brumbies, who travel to Melbourne to face the Rebels on Friday night in a pivotal clash, the Waratahs retain control of their finals fate.
The Tahs will be sweating over news on the injury front, though, after power forward Will Skelton joined the Waratahs' growing casualty ward.
The giant lock lasted just 36 minutes before succumbing to a shoulder injury and will have scans to determine if he joins fellow forwards Jack Dempsey, Jed Holloway and Benn Robinson on the sidelines before next Saturday's hosting of the Bulls at Allianz Stadium.
The Cheetahs had won their past encounters with the Waratahs in Sydney and, despite tasting victory just twice this campaign, the South Africans again proved nuisances.
- AAP
