England were put under pressure early in the game when New Zealand posted a daunting total of 146-5 in their allotted overs after rain relented in the series-decider.
Despite the stern test that awaited the visitors at the halfway mark of the match, the England camp was rather confident of chasing down the target according to Bairstow.
The wicketkeeper-batsman claimed several players from his side had participated in the T10 league in 2018 that assisted them to set up an exhibition of attacking strokeplay from the get-go.
Six of England's playing XI had made an appearance in the T10 last year in Sharjah as opposed to two of the Black Caps players.
"It was pretty imposing to try and chase down 150 but a lot of the guys played in the T10 last year and said we're not far off here and can get within striking distance with the small boundaries here," he told Sky Sports as he collected the man-of-the-match prize.
Bairstow fronted the batting charge with a spellbinding display of power-hitting before departing for an 18-ball 47 including five sixes and two fours.
Having failed to make an impactful contribution in the preceding games combined with a torrid run in Test cricket, Bairstow highlighted the importance of regaining his form.
"Obviously, it's nice to get some runs today. I don't feel like I have potentially scored as many as I would have wanted to during the series.
"To contribute in a shortened game - the pitch here is quite favourable for the batsmen so to get some runs was pleasing," he said.
Bairstow's dismissal derailed England's chase for a while but Chris Jordan's whirlwind cameo ensured scores were level at the completion of 11 overs.
Bairstow then walked out to bat in the crucial Super Over and struck a straight six off Tim Southee to lift his team to 17.
Jordan held his nerve to restrict the hosts to eight runs in reply as England clinched another win in a nail-biting thriller - four months after defeating New Zealand in similar circumstances in the World Cup final.
"We don't want to keep this [Super Over] happening," Bairstow added.
"I don't think anyone wants to keep that going but it just shows how close the sides are and how close they've been throughout the series and it sets up what's going to be a fantastic Test series."