India, set a revised target of 171 in 39 overs after rain delayed the start of their reply by nearly three hours, finished on 171 for one with 25 balls to spare.
Man-of-the-match Gambhir was 80 not out and fellow left-hander Ganguly 73 not out after batting star Sachin Tendulkar was bowled off the last ball of the first over by 26-year-old one-day international debutant Roger Whelan.
Earlier, India's teenage leg-spinner Piyush Chawla took a career-best three wickets for 29 runs as Ireland were bowled out for 193 in 50 overs.
The 18-year-old Chawla's figures, in his second match at this level, topped the three for 37 he took on debut against Bangladesh in Dhaka in May.
"It will be a long tour so it's important to start off well," Gambhir, 25 told reporters. For any cricketer, not just me, it's nice to start well and I'm pleased I got the runs.
"It's not like in India where you can just go out there and play through the line of the ball," added Gambhir after his 22nd one-day international.
"I toured England with India A so I know something about batting on these types of tracks. You want to start off a season on a high note and I'm happy about the way it's begun."
Ireland captain Trent Johnston, who made a valuable 34, said: "I thought we did pretty well to post 190 off 50 overs and the rain gave us 171 to defend which I thought was okay.
"Getting Tendulkar out first over, I thought something might happen here. I really did believe we had enough runs to do that but we just didn't ask enough questions and that was the disappointing thing."
Gambhir was not overawed by Tendulkar's early exit, clipping Whelan off his legs for four. He completed a 72-ball fifty featuring six fours before Ganguly reached the landmark, for the 68th time, in 79 deliveries.
The hosts were indebted to wicket-keeper Niall O'Brien's 52 and his stand of 48 with Johnston after they'd slumped to 121 for six following India captain Rahul Dravid's decision to field first.
Ireland, who produced the shock result of the World Cup when beating Pakistan and advancing into the second round - something India were unable to do after defeats by Bangladesh and Sri Lanka - had just six survivors from their team in the Caribbean.
They struggled against the swinging ball before Chawla bowled Gary Wilson for 13 to leave them 75 for four.
Chawla, the successor to Anil Kumble, now retired from one-day internationals, then removed Kevin O'Brien via a top-edged a sweep to RP Singh.
Andrew White became his third wicket, caught off a thick edge by Karthik and that meant the Australian-born Johnston came in with Ireland on 111 for six. Johnston though pulled Sreesanth for Ireland's first six, in the 41st over.
Meanwhile O'Brien, completed a 78-ball fifty by driving left-arm quick Singh for his fourth four. But next ball the left-hander got a leading edge and was caught by debutant Rohit Sharma.
This was India's first match of a tour that features three Tests and seven one-day internationals against England starting in July. Ireland are due to play South Africa in a one-day international here on Sunday.
India and South Africa then face one another in three one-day internationals at Stormont on Tuesday, Friday and a week on Sunday.