But Cardiff then had to endure a concerted fightback from the All Whites which began just 90 seconds after the break when Wales lock Andy Moore scored a try which was converted by Arwel Thomas, who had also landed three first-half penalties.
Even though Jenkins slotted a fourth penalty, Swansea inched closer over the next 20 minutes, with Thomas landing three more penalties. But Cardiff held on to a two-point lead - and in injury time they scored a third try when Simon Hill ran in for Jenkins to convert.
Despite their success, Cardiff are still four points adrift of leaders Pontypridd, who crushed Caerphilly 61-14 at Sardis Road. The chunky wing Lenny Woodard helped himself to two of Pontypridd's nine tries as they ran their uninspired guests ragged. The other wing, Gareth Wyatt, also dashed over twice, while Caerphilly's sole touchdown came from Justin Hughes.
Llanelli remain second following a comfortable 37-9 victory over Edinburgh Reivers at Stradey Park. Fly-half Stephen Jones kicked six penalties and two conversions while Ian Boobyer, Craig Warlow and Chris Wyatt each went over.
After losing three of their last four matches, Ebbw Vale fought back from 18-5 down against visitors Bridgend to win 26-18. Stephen John, Jon Hawker and Brad Clark went over for Vale while Jason Strange slotted a conversion and three penalties.
The third round of the Tetley's Bitter Cup produced its usual upsets, with at least five of yesterday's 16 ties resulting in victory for the junior side. Perhaps the most heartening from the traditionalist's viewpoint was the 28-7 success of Rosslyn Park, beaten finalists twice in the Seventies but now plying their amateur trade in Jewson League One, away to Wakefield of Allied Dunbar Premiership Two.
Two other Jewson One sides triumphed over struggling Allied Dunbar Two teams. West Hartlepool, a Premiership One club less than seven months ago, continued their descent into mediocrity by surrendering 28-7 at home to Bracknell, while Birmingham-Solihull squeezed past visitors Waterloo at home 18-15 after extra time.
Jewson One sides tasted their own medicine from Two North opponents when New Brighton ousted Otley 15-6 and Nuneaton saw off Camberley 29-19. Meanwhile, there was heartache for minnows Sevenoaks, who knocked out Blackheath in round two, when they lost 24-23 to Thurrock in extra time.Reuse content