Sparkling Fiji score four tries beat error-prone Scotland 29-14
The Fijians scored four tries and dominated a lively contest in hot conditions, sealing victory with a penalty try late in the match when Graham was shown a second yellow card for deliberate offside.
It was only Fiji's third win over the Scots -- all having been achieved in Suva -- while Scotland have won the other eight Tests between the two, including last November's 57-17 triumph in Edinburgh,
"It was tough for us when we were down to 14 men on three occasions, but Fiji deserved to win," Scotland head coach Gregor Townsend told BBC Sport.
"We're disappointed with our own performance and disappointed we didn't capitalise on a good start to the second half and getting back in the game.
"There were 14 penalties and three yellow cards. I would imagine most of them are in our control."
Scotland fielded a starting team featuring 14 changes from the side who opened their tour with a 29-26 defeat of the Maori All Blacks in Whangarei a week ago.
Fiji made just two changes from the team beaten 21-18 by Australia in the dying minutes in Newcastle.
Scotland scored a converted try early in each half but otherwise were forced into defence for long periods against a home side who mixed power and skill to good effect.
Too many mistakes
The Scots, who trailed 15-7 at half-time, missed 36 tackles and gave away 15 penalties.
"The start of the game and start of the second half showed what we can do," said Townsend.
"Some of the effort was excellent, but there were too many times where it was simple mistakes."
They made a bright start, creating a try in the third minute for fullback Kyle Rowe.
Their grip on the game slipped when hooker Ewen Ashman was shown a yellow card for a professional foul and experienced flanker Jamie Ritchie was forced from the field with injury.
Fiji fly-half Caleb Muntz slotted a penalty and his team took command in the period before half-time after Graham had been sent to the sin-bin for an early tackle.
Captain Tevita Ikanivere gave his team the lead through a lineout drive try before winger Kalaveti Ravouvou capitalised on an overlap to cross in the right corner.
Scotland responded after the interval through a try by centre Tom Jordan.
But a brilliant solo try from winger Jiuta Wainiqolo, followed by the penalty try, when Graham raced off his own line too quickly to intercept a pass, took Fiji to victory.
Referee Ben O'Keeffe deemed the wing had prevented a probable Fijian try.
Scotland complete their three-match Pacific tour when they play Samoa in Auckland on Friday.