Tries from Darren Sweetnam, Dave Kearney and Jack Conan gave Ireland a 17-3 lead after 35 minutes but five minutes after the break, Fiji had drawn level.
Henry Senioli and Timoci Nagusa ensured a nervous second half for the home side.
Ian Keatley came off the bench in a match riddled with errors and hit two late penalties to save the Irish.
Ireland were immensely good last weekend registering a record 38-3 win over the South Africans to commence their autumn international campaign in style.
Head coach Joe Schmidt opted to make 13 changes for this game, giving a range of fringe players the chance to impress.
But both individually and collectively they struggled to make the most of the opportunity as the intensity shown last week never came to fruition.
Eight players with five caps or less started for Ireland, and it showed.
There was a lack of unity and the unfamiliarity between players resulted in long periods of scrappy play from both sides.
Darren Sweetnam dotted down in the corner just seven minutes into his first international start following a superb break by Joey Carbery.
Andrew Conway followed up his impressive display against the Springboks with a Man of the Match performance at fullback and his effort allowed Dave Kearney to score in the opposite corner.
Jack Conan’s great pick-up off his boot and blistering pace produced another try – his fourth for Ireland in just five appearances.
Ireland were 17-3 ahead before the visitors had their best spell either side of the interval and Ulster’s Stuart McCloskey believes his side were fortunate to come out the victors.
“We were lucky to get away with the win there,” Stuart McCloskey told Sky Sports.
“Right now he (Ireland boss Schmidt) will be happy we’ve got the win. He’ll be looking back at a lot of mistakes and lot of turnovers.
Fiji lock Leone Nakarawa was understandably frustrated after the narrow defeat.
“Today it was a disappointing game for us,” the 29-year-old said.
“We didn’t play to our strengths. We didn’t play to our system and that’s a result that’s disappointing today.”
Ireland finish their autumn international series against Argentina on 25 November, and Joe Schmidt will probably waste little time in recalling his first-choice players.
