First five-eighths Lincoln McClutchie converted, as he did when flanker Miracle Fai’ilagi scored five minutes before halftime.
With Jacomb adding the second of his four penalties, becoming the top scorer in the 2025 NPC, it was 14-6 at halftime.
McClutchie had to step into halfback as Folau Fakatava was yellow-carded and Jacomb closed the gap to five points by the time the black-and-white No 9 jersey was back on the park.
McClutchie was rewarded with a try in the 52nd minute with a single piece of brilliance, gapping between the Taranaki fullback and flanker to score close to the posts, possibly the most telling part of the game, and with Taranaki also down to 14 men.
Taranaki had plenty of territory and possession but the Magpies’ defence wore the visitors’ imagination down and the game was made near enough to safe with flanker Sam Smith’s try 14 minutes from the end.
There were many heroes among the Magpies, including prop Hadlee Hay Horton, who was a late addition to the starting line-up with Pouri Rakete-Stones unfit to play.
Earlier in the weekend, Otago and Bay of Plenty advanced with wins in their quarter-finals.
On Sunday home side Canterbury needed extra time to beat a fired-up Counties Manukau 23-15, setting up a semifinal against Hawke’s Bay next Saturday (7.10pm) at Apollo Projects Stadium in Christchurch.