The star forward came on for the final half-hour in Montevideo, where he struck with a free-kick six minutes after being introduced to add to Maxi Gomez's first-half header.
Another substitute, Real Madrid midfielder Federico Valverde, sealed Uruguay's win with a fine strike.
Edinson Cavani also came off the bench for Uruguay, who open their Copa America campaign against Ecuador on June 16.
Fouls ruined the early flow of the game, although Uruguay goalkeeper Fernando Muslera was tested by a long-range Fidel Escobar strike.
But Gomez opened the scoring for the hosts in the 19th minute with his second international goal.
After a throw-in on the right, Giorgian De Arrascaeta's lovely cross was headed in by Gomez from close range.
Uruguay pushed following their opener and De Arrascaeta poked a rebound wide after Panama goalkeeper Luis Mejia could only parry a tame Nahitan Nandez shot.
There was a brief injury worry for Uruguay as Diego Godin went down clutching his arm before half-time, while Matias Vecino had a volley pushed around the post by Mejia.
Suarez needed little time to have an impact, scoring his 56th international goal in the 69th minute.
The star forward curled a wonderful 20-yard free-kick into the top corner, giving Mejia no chance.
Valverde wrapped up Uruguay's win in the 79th minute, brilliantly volleying into the bottom corner from 25 yards after a cross from the right was cleared into his path.