Fozzy Stack is keen to chart a possible Classic route with Zihba after he won so well at Dundalk on Friday evening.
The son of Choisir was heavily backed into 2-9 favouritism for the one-mile Jimmy McGeough Median Auction Race.
And though Irish Minister kept him honest, Zihba lengthened smartly inside the final furlong to score by two lengths.
He is now unbeaten in two starts and holds an entry in the Irish 2,000 Guineas at the Curragh on May 26.
Stack said: "He did it well. He's still a work in progress and he probably needed the run a bit there with all the hold-ups with the weather. He did it quite well as he was giving the runner-up 15lb.
"Chris (Hayes, jockey) said he just gave a bit of a heave with him about two and a half (furlongs) down and then got his second wind and ran on. He'll probably go for a Guineas trial somewhere. I'd say he wants fast ground."
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