Accompanied by bodhran-playing male backing dancers, Dolan (27), from Strabane in Co Tyrone, got a huge cheer from the audience of almost 15,000.
His up-tempo song 'Only Love Survives' contrasted well with the ballads performed before and after him.
Last year's winner Loreen opened the first semi-final with a stunning version of her winning song 'Euphoria'.
Swedish host Petra Meade joked that one of the slogans organisers considered for this year's contest was: "Don't complain -- Norway is more expensive."
RTE's Eurovision commentator Marty Whelan said the semis were always tense.
"The semi-finals are desperate. We don't have the joy of the voting, there are just names and you're waiting for them to tell us who it is," he said.
Now in his 14th year commentating on the show, he believes Ireland has firmly got its passion for Eurovision back.
He said: "You have to come in with an optimistic attitude. If you don't go in with that, why bother?"
The second semi-final takes place on Thursday night and the grand final is on Saturday.
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Someone will break a promise to you, which is disappointing. Don't let this setback stop you from crossing the finish line. You may have to submit an entry late or attend the last few minutes of a meeting, but take heart. Rallying in the midst of difficult circumstances will count in your favour. Someone else may get a job or scholarship, but you'll be in the running for the next opportunity. In the meantime, have an alternative plan ready when relying on others for help.More