Brandon Haunstrup’s drive through Adam Legzdins’ legs with 14 minutes left has given the top-flight team a lifeline.
Wright admits Dundee will believe they are in the “driving seat” but had to declare himself satisfied with the result after his side were second best for long spells at a wet and windy Dens Park.
Kilmarnock turned round a one-goal deficit at the same play-off stage against Falkirk in 2016, winning the second leg 4-0 after a 1-0 defeat in the first game. They host Dundee on Monday night.
“I'm pleased we've got ourselves back in the game,” said Wright. “They were using the conditions better than us and were in control at 2-0.
“They will be disappointed that they have conceded but will still probably feel they are in the driving seat. But it's a massive goal for us in the context of the two legs and puts us right back in the tie. I don't want to take anything away from Dundee as they played well.
“But looking at my own team's performance, they are disappointed with how they played. I'm just so pleased we got that goal back because it makes things a little bit easier. It's still going to be difficult to turn things around and they are probably favourites.
“The quality has got to be better but the character is there,” he added. There are pundits out there who have hammered their character, but I've never doubted it. I'm hoping that's going to be a big turning point in the tie.”
James McPake praised his side’s performance after Dundee restricted the visitors to just one shot on target all night. He was particularly pleased to see Dundee fan and skipper Charlie Adam scored his side’s second goal at the home end at Dens, where 500 Dundee fans had been permitted entry.
“The very first minute he gets a chance to score a goal in front of Dundee fans- I know he scored at Crystal Palace - he does it,” he said. “But it will only be extra special if we finish the job on Monday night.”