Ireland made most of the running during the first half, with the impressive Jeff Hendrick drawing a sharp save from Andreas Isaksson before rattling the Sweden goalkeeper's crossbar.
Hoolahan also shone and the Norwich City midfielder would pip Hendrick to the man-of-the-match honours by crashing home a fine opener on the end of Seamus Coleman's cross - sparking delirium among the massed ranks of green-clad fans inside the Stade de France.
Sweden produced a determined response and, although Ireland shackled Zlatan Ibrahimovic impressively for the most part, the superstar forward powered past John O'Shea in the 71st minute and his cutback was diverted in by unfortunate Republic defender Ciaran Clark.
"I'm pleased with the performance, we played really well - created a lot of chances in the first half and went ahead in the second half," he said.
"They got the equaliser, which was a bit disappointing but overall we are proud of our performance.
"It was a good performance and we look forward to playing Belgium on Saturday."
On the sweet strike with his weaker right foot, Hoolahan added: "Seamus did brilliantly to beat his man and it was great to score.
"We started on the front foot and pressured them a lot of times during the game, then fatigue probably set in a little bit.
"Overall the performance that we delivered was very good."