A breakdown infringement led to Mallow losing their player-coach Taukiri to a seventh-minute sin-binning but they recovered well to lead 14-12 at the half-time interval.
Number 8 Cliff Cahill slipped through the Dromore defence, three minutes later, and while he was stopped short of the try line, winger Rory McSherry showed good awareness to pick and go off the resulting ruck and score under the posts.
Centre Cashman added the extras but Dromore reduced the arrears to two points when, in the 20th-minute, Mark Crothers gathered up the ball to score after a clearance kick from Mallow had been charged down.
The conversion was missed and Dromore's player-coach Neil Doak, the former Ulster scrum half donned the number 10 shirt for his club, stepped his way past a number of would-be tacklers for a try, the visitors still led at the break.
On the 37-minute mark, Dromore lost control of a scrum near their own line and the ball squirted free of the set piece for Mallow scrum half Kevin Twomey to gleefully touch down - James Cleland converted.
Against the wind, the Munster Junior League Division Two side strengthened their lead when Cashman swung over a penalty on the resumption.
Then Dromore dramatically upped the tempo, their pack worked through phase after phase and eventually Rory Pepper got over for the hosts' third try, levelling the score at 17-all.
By that stage, the north Down outfit should have been ahead - Doak narrowly missed out on his second try as his kick ahead just rolled over the end line as he went to ground the ball.
In reply, Jerry Cronin played the captain's part for Mallow as he offloaded for outside centre Des Golden to bag a converted try.
A Cleland penalty cut the gap to four points and Dromore took the lead - 25-24 - when Johnny Penny 'cashed' in on a superb blindside move from the hosts' pack to notch their fourth try.
Mallow though had one last trick up their sleeves and Cashman held his nerve over a difficult kick to boot the Cork men into the last-four.
Remainder of the quarter-final reports to follow...
Coleraine 45 Boyne 17, Sandal Lodge Park (after extra-time)
Crosshaven 14 Armagh 6, Myrtleville Cross
Dromore 25 Mallow 27, Dromore
Seapoint 32 Limavady 18, Kilbogget