The lock added to his scores against the Scarlets on the opening weekend of Ulster’s Pro 12 campaign and in last week’s rout of Zebre to help the visitors maintain their unbeaten start to the season.
Paddy Jackson kicked 14 points on his first start of the season, the 22-year-old impressing against an improved Blues side following their heavy defeat by Glasgow the previous week.
Out-half Jackson put the visitors in front with a long-range penalty after eight minutes following a frantic opening from both sides.
Cardiff drew level on 22 minutes when a swift attack from scrum-half Lewis Jones forced the visitors to concede a penalty inside their own 22 and full-back Rhys Patchell slotted over.
Ulster almost had the game’s opening try when number eight Nick Williams broke clear and was supported well by Tommy Bowe and Paul Marshall but Blues flanker Josh Navidi eventually disrupted the chance.
Patchell put the Blues in front for the first time with a second penalty after fine work from his forwards at the scrum, but the lead lasted just three minutes as Jackson kicked another three points.
Jackson then gave Ulster the advantage with a third penalty after a needless obstruction by Blues centre Gavin Evans. Evans did atone for his mistake shortly after, winning a penalty inside the Ulster half which Patchell kicked with ease.
Ulster snatched back the lead on the stroke of half-time and again it came via the boot of Jackson.
Patchell had a chance to restore parity five minutes into the second period but his accuracy let him down from near halfway before Jackson missed his first kick of the night from a similar position shortly after.
But a poor clearance from Blues outside half Gareth Davies handed Ulster a line-out in a dangerous position and from the set piece they went through four phases before Marshall popped a short ball up to lock Tuohy and he went under the posts.
The Blues should have hit straight back when they dragged the Ulster defence from one touchline to the other but at the crucial moment Patchell’s pass to wing Richard Smith was behind him and he could only fumble into touch.
Replacement Ian Humphreys compounded the Blues’ misery when he collected a speculative long pass from fly-half Davies to saunter over five minutes from the end before adding the extras himself.
Cardiff Blues scorers: Pens: Patchell 3.
CARDIFF BLUES: Patchell, Cuthbert, A. Thomas, G. Evans, Smith, G. Davies, L. Jones, Hobbs, Rees, A. Jones, Hoeata, Paulo, Turnbull, Navidi, Vosawai.
Replacements: Walsh for Patchell (77), L. Williams for L. Jones (55), Andrews for Hobbs (58), R. Williams for Rees (64), Filise for A. Jones (53), Allen for Hoeata (57).
Ulster scorers: Tries: Tuohy, Humphreys. Cons: P. Jackson, Humphreys. Pens: P. Jackson 4.
ULSTER: Ludik, Trimble, Cave, Olding, Bowe, P. Jackson, P. Marshall, Warwick, Best, Herbst, Tuohy, van der Merwe, Diack, Henry, Williams.
Replacements: Humphreys for Cave (60), Gilroy for P. Jackson (61), Black for Warwick (41), Herring for Best (76), McComb for Tuohy (61), Wilson for Williams (60).
Referee: Neil Paterson (SRFU).