Rhys Lawrence replied for the visitors soon after though, handing his side an 8-7 lead at the interval.
An Adrian Thomas penalty edged Llangennech back in front on the hour-mark, but it was Tiueti who crashed over for the match-sealing try 15 minutes from time to keep Tonmawr on track for the title.
Carmarthen Quins remain in hot pursuit of the leaders after a strong second-half performance saw them defeat Bonymaen 24-10.
With the scores locked at 10-10 at the interval, after Quins winger Dan Gravell and Bonymaen's Christian Gibbins had exchanged scores, the home side dug deep in the second half and further tries from flanker Andrew Thomas and centre Dan Rogers, both converted by Mark Jones, saw them home.
Narberth capitalised on Llangennech's loss to leapfrog them into third place after beating Merthyr 13-0. All the points came in the first half as No.8 Lloyd Phillips and right wing Tom Bonnell claimed tries while Aled Davies kicked a penalty.
Basement boys Corus registered only their second win of the campaign as they beat fellow strugglers Waunarlwydd 24-14. Bleddyn Gant, Neil Holgrove and Chris Macdonald were amongst the tries in a win that puts them level with Waunarlwydd on 13 points.
Elsewhere there were wins for Bridgend Athletic and Cwmllynfell over Whitland and Dunvant respectively.
The Division One East programme was disrupted by the weather with only the games at Beddau and UWIC surviving.
At Beddau, Caerphilly walked away with the spoils as tries from Gary Miles and Lee Mullane gave them a 20-12 victory. The hosts did go over for two tries of their own through Nathan Walters and Craig Warman but 10 points from the boot of Caerphilly's Chris Ashton were enough to move his side up to third in the table.
At the Cyncoed Campus, second-placed Bargoed had too much for the students as they recorded a 30-14 bonus point win.