Both fell in the seventh and ninth overs – Malan for 23 – as the score fell to 69-3 before Tom Kohler-Cadmore, Harry Brook and Will Fraine saw their side home with nine balls left.
Jordan Thompson equalled a career best 3-23 from four overs of seam as the Bears stuttered to 144-8, with Sam Hain’s 59 off 41 holding things together.
Matthew Waite had Will Rhodes and Adam Hose caught off miscues as Birmingham slipped to 29-3 inside four overs having been inserted.
Hain came in at six for two in the second and hit three sixes before falling midway through the final over to David Willey.
He shared 33 for the fourth wicket with Dan Mousley and 49 for the seventh with former home favourite Tim Bresnan, who made 23 to advance from 89-6 in the 13th over on a true pitch.
Adil Rashid and New Zealand debutant Lockie Ferguson were outshone by all-rounders Waite and Thompson as all Bears wickets were caught.
Waite opened the bowling and returned a career best 2-36, while Thompson’s haul included two caught and bowleds.
One was a superb diving effort to dismiss West Indian Carlos Brathwaite cheaply.
Yorkshire lost Adam Lyth four balls into their chase to Danny Briggs’ left-arm spin.
But Bairstow slog swept him for six over midwicket in the third over before Malan clipped and cut successive boundaries off Brathwaite in the next to get the Vikings rolling.
Bairstow, making his first Blast appearance since Finals Day 2016, pulled Bresnan for two sixes before the all-rounder had Malan tamely caught at midwicket.
Bairstow then chopped on to Briggs in the ninth over – the next from the Emerald Stand End – as the Vikings slipped to 69-3.
But they never realistically looked like encountering serious danger in front of a boisterous 4,000 crowd.
Kohler-Cadmore and Brook (24) shared 49 before the latter fell to Brathwaite, leaving the score at 118 for four after 16.1 overs.
Kohler-Cadmore finished 31 not out before Fraine crashed 19 off eight balls, including the winning runs.
Reflecting on the home victory, batsman Fraine said: “It’s good to get off the mark and get that first win in the bag.
“With the side we’ve got, we were coming into this game really confident.
“It was a good pitch, but we managed to restrict them well.
“You never know with those chases, and I would be lying if I said there weren’t a few nerves when I went out to bat. But everyone is buzzing.
“There’s some crazy stat that if you lose three wickets in the power play, you lose something like 80 percent of your games. I think we bowled great up top.”
Birmingham spinner Danny Briggs said: “Looking back, we were a little bit short with the bat. But, in the first game of the tournament, there were positives there.
“We managed to get a score with the bat and scrapped really well with the ball and in the field. The beauty with Twenty20 is that we’ve got a game tomorrow night and we can put that right straightaway.”
“It wasn’t too bad for me (two for 28), but I would have liked it to be in a winning cause.”
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