After Afghanistan made 182-6, New Zealand were driven by Seifert's 42-ball knock and 42 by Glenn Phillips to achieve their target with 13 balls to spare in Chennai.
New Zealand's previous best chase in the T20 World Cup was their 167 against England in the 2021 semi-final.
"It's always nice to start the tournament with a few runs under your belt, but the main thing is we got the win," player of the match Seifert said.
"Tough conditions as well out there. Lost a couple of early wickets, so it's nice to get the job done."
Afghanistan spinner Mujeeb Ur Rahman had New Zealand in early trouble when he struck on successive balls in the second over of the chase to dismiss Finn Allen, for one, and Rachin Ravindra, for a duck.
The hat-trick was avoided by Phillips, who then got going with wicketkeeper Seifert in a partnership of 74 for the third wicket to thwart Afghanistan's spin-heavy attack.
Captain Rashid Khan let out a roar as he broke through to dismiss Phillips, who inside-edged onto his stumps.
Leg-spinner Rashid dropped Seifert on 48 off his own bowling and the batsman reached his fifty with a six off veteran spinner Mohammad Nabi.
Seifert hit Nabi for another six and a four on successive balls before the bowler had his revenge on the next when he top-edged to be caught in the deep.
Mark Chapman fell after a 17-ball 28 but Daryl Mitchell, on 25, and skipper Mitchell Santner, on 17, saw New Zealand to 183-5 and a comfortable victory.
"We haven't landed the ball in the right areas," said Rashid.
"If we had bowled into the wicket and good length it was difficult to score. We need to improve in certain areas."
Afghanistan won the toss and chose to bat and Gulbadin Naib, coming in at number three, struck 63 off 35 balls as after they had slipped to 44-2.
Matt Henry nearly had Rahmanullah Gurbaz caught after he skied a top edge behind the stumps, but keeper Seifert and Allen collided as they both ran back and the chance went begging.
Pace bowler Lockie Ferguson struck twice in his opening over to send back Ibrahim Zadran, for 10, and then Gurbaz, bowled for 27 off an inside edge.
Naib and left-hander Sediqullah Atal, who made 29, got together to rebuild the innings with a 79-run stand for the third wicket.
Naib reached his fourth T20 fifty off 29 balls before he departed attempting a slog off left-arm spinner Ravindra.