Unlike the Golden Lions in Johannesburg three days earlier, Cheetahs refused to take a mauling.
The Lions eased into cruise control during a one-sided opening quarter after tries by flanker Stephen Ferris and centre Keith Earls helped open up a 17-0 lead.
Cheetahs, though, struck twice in seven first-half minutes after Ferris was sin-binned by English referee Wayne Barnes, with wing Danwel Demas and prop Wian du Preez claiming touchdowns that Jacque Potgieter converted.
Centre Corne Uys then struck with an 80-metre interception try eight minutes from time that substitute Louis Strydom converted, setting up the prospect of a famous home win.
Lions wing Shane Williams could only look on after Uys collected his intended pass to fly-half James Hook - but there were more scares for the Lions to survive before full-time.
Strydom was agonisingly wide with a drop-goal attempt which would have sealed the deal, then the Cheetahs were unable to prosper from an attacking scrum after Lions full-back Lee Byrne uncharacteristically spilled a high ball.
Ultimately, the Lions were indebted to Wales star Hook's precision goal-kicking to maintain their unbeaten record.
Hook, who looks set to mount a serious challenge for the Test team number 10 shirt, booted four penalties and two conversions - an immaculate return which kept Cheetahs at bay.
The tourists made a lively start, looking to keep possession alive, but a knock-on by lock Donncha O'Callaghan sacrificed a promising attacking position deep inside the Cheetahs' 22.
A juggernaut Lions front row of Andrew Sheridan, Ross Ford and Euan Murray looked to make their mark, but the game's second scrum disintegrated into a brawl.
Ferris and Cheetahs lock Nico Breedt wrestled on the floor while several other players also got involved before Barnes warned Murray and his opposite number du Preez.
Hook hoisted the Lions ahead with a 40-metre penalty after seven minutes, but the visitors were already embroiled in a far more fierce encounter than at Ellis Park on Wednesday night.
Hook's opposite number, Potgieter, missed a long-range penalty chance and the Lions responded by catching the home defence asleep.
Cheetahs failed to clear 30 metres out and Ferris reacted quickest, gathering possession and sprinting unopposed to the line for a try which Hook converted.
It was Ferris' second touchdown of the tour, putting him one behind leading try-scorer, Tommy Bowe, as the Lions began to take a firm grip on proceedings.
With a one-sided opening quarter reaching its conclusion, the Lions struck again.
Hook's delightful kick into space was collected by Earls, who showed a blistering turn of pace to leave the Cheetahs' defence for dead. Hook added the extras.
Ferris then blotted his copybook by receiving the Lions' first yellow card on tour, leaving Barnes with little option when he prevented quick Cheetahs ball from being released.
Down to seven forwards, the Lions found themselves under mounting pressure, even though a second Hook penalty had extended their advantage to 20-0.
But their opponents made their temporary one-man advantage count after good work by the pack helped create an overlap for Demas. Potgieter converted.
They almost scored again just six minutes later, when Demas agonisingly failed to gather his kick ahead and the Lions escaped.
It was only a temporary reprieve, though, and, with Ferris still off, workaholic du Preez stormed over for a try Potgieter improved.
Ferris' caution had proved costly - 14 points conceded while he was absent - and the Lions needed to tighten up considerably as half-time approached.
Hook's third successful penalty gave them an element of breathing space, yet the Lions knew they were in a real contest at just 23-14 ahead.
Potgieter cut the gap to six points when he rifled over a 45-metre penalty after Leigh Halfpenny was penalised for an illegal challenge.
The Lions struggled to impose their rhythm and cohesion so evident during the first 20 minutes as frustrating errors crept in, especially around the forward fringes.
Hook landed a sixth successful kick from six attempts - his fourth penalty - for a 26-17 advantage after 50 minutes.
However, Cheetahs were belying their status as the Super 14's last-placed team this season, and the closing minutes were high-octane stuff.
The Lions could easily have lost and, on the evidence of their second-half display, there could have been few complaints - but the hosts just lacked composure to steal victory and a momentous day in their history went begging.
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