Otago eventually got their reward as a nice inside ball from Kayne Hammington put Freedom Vahaakolo in untouched under the posts.
Hawke's Bay finally got some ball and made full use of it, with winger Neria Fomai busting a tackle to score a try in the corner with half an hour played.
Vilimoni Koroi missed a fairly simple shot at goal as the wind died down and the Magpies seized the momentum.
Fullback Lolagi Visinia won the race to a Stacey Ili grubber kick through, scoring a try in the 35th minute of his blazer match.
Hawke's Bay were now playing with full confidence, and almost had a third five pointer right on halftime but knocked the ball on.
Otago had the first say of the second half when Koroi chipped over a penalty inside two minutes.
The Magpies turned down their own easy shot at goal for an attacking lineout, however conceded a penalty for holding on close to the tryline.
They made up for it though, with centre Stacey Ili beating his marker to score out wide and put Hawke's Bay nine points ahead with less than half an hour remaining.
Substitute flanker Josh Kaifa got the bonus point try as Hawke's Bay began to show the electric attacking form fans were treated to last season.
Man of the match Jonah Lowe sealed the deal on fulltime with a brilliant chip-and-chase individual try.
It was far from a complete performance but the win lifted the Magpies towards the top four in the NPC Premiership, putting the rest of the competition on notice.
Head coach Mark Ozich said his side won the game thanks to their tenacious defence in the opening 30 minutes.
He said earning a halftime lead allowed the Magpies to show their attacking flair after the break:
"Still not quite there, but we're starting to get into a rhythm."
Ozich said flanker Solomone Funaki gave his team exactly what they needed at the breakdown and also praised the work of back three Jonah Lowe, Neria Fomai and Lolagi Visinia on both sides of the ball.
The coach confirmed that Dixon missed the game having battled illness all week, while McLeod looked to have damaged ligaments in his knee during the warmup.
McLeod's injury will keep him out for most of the season, so Ozich said he may have to recruit a new halfback.
In the curtainraiser, Hawke's Bay Tui defeated Tasman 80-5 for their second win of this year's Farah Palmer Cup, leaving them second in the Championship division through five rounds.
AT A GLANCE:
Hawke's Bay 34 (Fomai, Visinia, Ili, Kaifa, Lowe tries; McClutchie 2/3 cons; Falcon 1/2 con, 1/1 pen)
Otago 10 (Vahaakolo try; Koroi 1/1 con, 1/2 pens)
HT: 14-7