Returning to his old ground, 40-year-old goalkeeper Rab Douglas made life uncomfortable for Celtic with a string of stops.
None were finer than his leaping save from captain Scott Brown’s penalty kick in the first half.
Douglas, who also saved a penalty away to Hearts this season, was praised by both managers after the game, which ended 2-0 to the hosts.
Dundee manager Barry Smith said: "Rab has done extremely well for us all season.
"He gets a lot of plaudits and maybe a lot of people give him some stick but at 40 years of age, producing performances week in, week out is difficult.
"For him to continue to do that is great for Dundee Football Club."
Opposing manager Neil Lennon, who played with Douglas in the successful Martin O’Neill Celtic side of the 2000s, joked: “I will have him by the neck later on for making my day uncomfortable.
"I thought he was excellent. It took two quality goals to beat him.”
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