Taranaki dominated the opening half an hour after the team got out to a healthy 19-0 lead.
The lead was commended by captain Teihorangi Walden.
"It was all we talked about during the week, a good start. We played some smart rugby, played down there and our defence kept us down there," he told Sky Sport.
"We couldn't have asked for a better start; Hawke's Bay have been the benchmark for the comp [competition] for a few years."
Walden also credited the defence, but said the team's discipline was a work-on heading into next week.
The opening try included an old-fashioned driving maul that allowed Bradley Slater to score. Fitting as Taranaki played in a retro-style jersey commending the 1996 Ranfurly Shield win 25 years ago against Auckland.
Referee Jono Bredin wanted to confirm the try with television match official Max O'Leary, which was eventually awarded.
Adding to the points were three first-half penalty kicks from fullback Stephen Perofeta. He kicked well off the tee during the match and added three conversions and another penalty to his name.
But Hawke's Bay managed to get into Taranaki's 22 and scored after a long buildup.
It was Lincoln McClutchie who sliced the Taranaki defence to score under a penalty advantage.
Just on the stroke of halftime, Hawke's Bay scored again through a rolling maul. It provided No.8 Devon Flanders with a good platform to keep control of the ball at the back.
With the score at 19-12 at the break, Taranaki scored inside the opening 10 minutes of the second half.
Slater crossed again despite protest from Hawke's Bay captain Ash Dixon to go upstairs.
Solid Hawke's Bay defence in their own half forced Taranaki to knock the ball on and 10 minutes later, they were deep in the home team's half.
Dixon crossed over for the try from a rolling maul after they were denied twice before.
After Hawke's Bay's attempted probe at the line, Taranaki's defence forced a turnover, which pushed the visitors into midfield.
A Jayson Potroz tackle forced a Hawke's Bay turnover, which then allowed Tikoisolomone to show his speed down the outside to have the final say – backing up his reputation of a try-scoring machine for Border.
Meanwhile, in Albany, the Taranaki Whio lost 24-12 against North Harbour.
Taranaki were leading at the break, but a second-half surge for the home team allowed them to pick up their second win of the season.
Taranaki 33 (Vereniki Tikoisolomone, Bradley Slater 2 tries; Stephen Perofeta 3 con, 4 pen)
Hawke's Bay 19 (Lincoln McClutchie, Devan Flanders, Ash Dixon tries; Lincoln McClutchie con, Tiaan Falcon con).