The Premiership side fell behind as Fiji, determined to bounce back from their heavy defeat to England at the weekend, raced into an early lead.
Hooker Tuapati Talemaitoga and winger Timoci Matanavou went over to open up the sizeable advantage with 33 minutes on the clock.
But a change in tactics helped Gloucester and they got back into the game before the break, flanker Matt Cox scoring a try to end the half just eight points back.
Fiji again delivered the first blow after the interval, through winger Watisoni Votu, before a couple of penalty tries saw Gloucester move to within two points at 26-24 with 10 minutes remaining.
Fiji edged ahead through Jonetani Ralulu's fourth penalty only for Koree Britton to go over and draw the English side level. Dan Robson's conversion gave them the lead and, despite some late chances for the tourists, victory.
In Leicester, George Ford starred as the Tigers became the first team to beat the Maoris in more than five years.
Fly-half Ford ended the evening with a 22-point haul having kicked eight of 10 attempts - a marked improvement on his last start against Northampton, when he only managed five from nine.
Matthew Tait started his first match in 13 months as he continued his recovery from a serious groin injury, and it was the England international's floated pass to Niall Morris that led to Leicester's opening try.
Adam Thompstone also went over for the Tigers while the Maoris - who included four full All Blacks in their line-up - scored three, Frae Wilson, Tim Bateman, Charlie Ngatai getting on the scoresheet.
But Ford's kicking kept the hosts' noses in front as the Maoris kicked off their tour of the UK with a rare defeat.