The Dane, Cardiff's top scorer last season, had seen an early effort ruled out for off-side and then found Burton keeper Stephen Bywater in fine form.
But with three minutes left Zohore held off two defenders to curl a shot home.
Burton could have led in the first half when Marvin Sordell's goal-bound shot was blocked, but had to thank Bywater after half-time as Cardiff dominated.
Luck had not been with Nigel Clough's side this week with Liam Boyce suffering an anterior cruciate ligament injury that will keep the striker out for most of the season.
But Burton were thankful to survive an early scare when Zohore pulled away at the back post to turn in Joe Bennett's cross, only to be flagged for off-side.
Zohore had an even better chance after being played through by Lee Tomlin, but shot wide across Bywater's goal.
Burton should have scored as the game sparked to life just before the break, only for Sol Bamba's last-ditch tackle to deny Sordell from Lloyd Dyer's pull-back.
Cardiff started the second half with more urgency and - cheered on by 1,700 travelling fans in a 5,050 crowd at the Pirelli Stadium - soon created a chance for Junior Hoilett, whose shot deflected just wide of the near post.
From the resulting corner Bywater pulled off a fine save to stop Bamba's powerful effort. The defender was proving a real nuisance for Albion and Bamba again got free from a free-kick, but headed straight at Bywater.
The Bluebirds turned the screw as Cardiff boss Neil Warnock made attack-minded changes and Hoilett's header was deflected wide, Zohore's shot was tipped over and Mendez-Laing blazed wide when well placed.
But just as Albion, again tipped as one of the relegation favourites, looked to have battled to a point, Zohore bullied his way into the area to give Warnock a perfect start to his 50th year in football.
Burton manager Nigel Clough:
"In the second half they put us under a lot of pressure. They put a lot of balls into the box and it has taken a brilliant finish to beat us in the end.
"There is not much you can do when someone rifles one in the bottom corner from 20-odd yards out.
"I thought for the way we defended we deserved a point and I thought we dealt with things very well and we missed our opportunity in the first half if anything."
Cardiff manager Neil Warnock told BBC Radio Wales Sport:
"It's a great way to start and you could see the optimism, the fans were fantastic today and kept us at it. The volume was unbelievable.
"I tried to be positive with my changes, I made positive subs, because I wanted us to try and win the game.
"I felt at half-time we had to do a little bit more going forward... I think the changes helped with that."
Match ends, Burton Albion 0, Cardiff City 1.
Second Half ends, Burton Albion 0, Cardiff City 1.
Foul by Luke Murphy (Burton Albion).
Nathaniel Mendez-Laing (Cardiff City) wins a free kick on the right wing.
Corner,  Cardiff City. Conceded by Stephen Warnock.
Foul by Luke Varney (Burton Albion).
Sean Morrison (Cardiff City) wins a free kick in the defensive half.
Lucas Akins (Burton Albion) wins a free kick in the defensive half.
Foul by Aron Gunnarsson (Cardiff City).
Substitution, Burton Albion. Joe Sbarra replaces John Mousinho.
Attempt blocked. Kenneth Zohore (Cardiff City) left footed shot from outside the box is blocked. Assisted by Loïc Damour.
Goal!  Burton Albion 0, Cardiff City 1. Kenneth Zohore (Cardiff City) left footed shot from outside the box to the bottom left corner. Assisted by Loïc Damour.
Attempt missed. Nathaniel Mendez-Laing (Cardiff City) right footed shot from the right side of the six yard box is high and wide to the left. Assisted by Loïc Damour with a cross following a corner.
Corner,  Cardiff City. Conceded by Jake Buxton.
Attempt blocked. Danny Ward (Cardiff City) left footed shot from the centre of the box is blocked. Assisted by Nathaniel Mendez-Laing.
Attempt missed. Nathaniel Mendez-Laing (Cardiff City) right footed shot from the right side of the box is high and wide to the right. Assisted by Loïc Damour.
Substitution, Cardiff City. Danny Ward replaces David Junior Hoilett.
Substitution, Burton Albion. Luke Varney replaces Lloyd Dyer.
Offside, Burton Albion. Lloyd Dyer tries a through ball, but Matthew Lund is caught offside.
Corner,  Burton Albion. Conceded by Joe Ralls.
Attempt blocked. Matthew Lund (Burton Albion) right footed shot from outside the box is blocked.
Attempt blocked. Hope Akpan (Burton Albion) left footed shot from the right side of the box is blocked. Assisted by Jackson Irvine.
Jackson Irvine (Burton Albion) wins a free kick in the defensive half.
Foul by Aron Gunnarsson (Cardiff City).
Lucas Akins (Burton Albion) wins a free kick in the attacking half.
Foul by Joe Bennett (Cardiff City).
Corner,  Cardiff City. Conceded by Stephen Bywater.
Attempt saved. Kenneth Zohore (Cardiff City) header from the centre of the box is saved in the top left corner. Assisted by Sean Morrison with a headed pass.
Corner,  Cardiff City. Conceded by Kyle McFadzean.
Attempt blocked. David Junior Hoilett (Cardiff City) header from the left side of the six yard box is blocked. Assisted by Nathaniel Mendez-Laing with a cross.
Attempt blocked. Nathaniel Mendez-Laing (Cardiff City) left footed shot from the right side of the box is blocked.
Attempt saved. Kenneth Zohore (Cardiff City) left footed shot from the right side of the box is saved in the top left corner.
Delay over. They are ready to continue.
Substitution, Cardiff City. Loïc Damour replaces Lee Tomlin.
Substitution, Cardiff City. Nathaniel Mendez-Laing replaces Bruno Ecuele Manga.
Substitution, Burton Albion. Hope Akpan replaces Marvin Sordell.
Delay in match Stephen Warnock (Burton Albion) because of an injury.
Attempt saved. Sol Bamba (Cardiff City) header from the centre of the box is saved in the top centre of the goal. Assisted by Lee Tomlin.
Foul by Luke Murphy (Burton Albion).
Lee Tomlin (Cardiff City) wins a free kick in the attacking half.
Kenneth Zohore crushed Burton Albion's resistance with a late goal to give Cardiff City an opening day victory.