Tunisia trailed 1-0 at halftime in the final Group G match in Saransk despite having the better of play. Fakhreddine Ben Yousseff equalised just after the restart with a neatly-taken goal and Wahbi Khazri scored a second to end Tunisia's long drought.
The result brought some vindication for the North Africans, who coach Nabil Maaloul had admitted before the game were demoralised after their defeats by England and Belgium.
But it was tough for Panama, making their first appearance in a World Cup finals, and for their fans in the Monrovia Arena who for a while could dream of a historic win.
"We wanted to snatch this victory, and I wanted to score, and I did. This is a great day for Tunisia," said man of the match Ben Yousseff.
Tunisia played fluent football but Panama took the lead after a shot by Jose Luis Rodriguez took a deflection off Tunisian defender Yassine Meriah in the 33rd minute for an own goal.
Having failed to finish off several chances in the first half, Tunisia took six minutes to assert themselves after the restart. Ben Yousseff picked up a low cross from Khazri to slot the ball home from close range.
Khazri added the second in the 66th minute, running unmarked on to a low cross to tap into an open goal.
Panama suffered when captain Roman Torres, who had marshalled the defence well, departed with an injury early in the second half.
ANXIOUS MOMENTS
Still, they pushed hard for an equaliser and caused anxious moments for Tunisia as the clock ticked away but lacked the killer instinct.
The two teams had already been eliminated from the tournament before the match started, both having lost to England and Belgium. But the spirited duel and the fervour of the more than 37,000 fans in the Mordovia Arena belied the notion that this was a pointless match between two lowly nations.
The Eagles of Carthage, making their fifth appearance in the World Cup finals, had not won a game since beating Mexico in Argentina in 1978 to become the first African country to notch up a victory at the tournament.
"Perhaps in the second match we should have been better. Our performance against England was very good...we should have been more defensive against Belgium," Tunisia coach Maaloul said.
Tunisia joined Saudi Arabia, Morocco and Egypt in failing to break out of the group stage while Panama fly home as one of only two nations to lose all three games and with the most goals conceded.
But coach Hernan Gomez says Panama have learned massively from the experience in Russia.
"We were much more level in this match than in others," he said.
(Reporting by Angus MacSwan; Additional reporting by Sudipto Danguly and Andrew Cawthorne, Editing by Ed Osmond)
