Monumental when his low, left-footed shot from the right beat the diving Justo Villar and went in off the far post.
Forlan, the 2010 World Cup's best player, made it 2-0 three minutes before halftime when he ran onto a ball from midfielder Egidio Arevalo Rios and blasted left-footed past Villar from just inside the box penalty box.
In the last minute, Forlan made sure of the title with his second goal at the end of a fine counter-attacking move, steering the ball past Villar and in off the post.
"I think Uruguay have achieved many things and needed not to forget how to win titles," Suarez told reporters.
Uruguay now have one more title than hosts Argentina, whom they upset on penalties in the quarter-finals, to crown a fine 12 months after their fourth place at the World Cup.
Twice champions Paraguay finished the tournament without a victory having reached the final with five draws and two penalty shootout wins.
Suarez scored four goals in the tournament, one less than top scorer Paolo Guerrero whose hat-trick helped Peru beat Venezuela 4-1 for third place in La Plata on Saturday.
Forlan, who won a Uruguayan record 82nd cap, ended a year without scoring for his country with his two goals and equalled the national record of 31 held by Hector Scarone.
'WC qualifiers tougher than Copa'
Winning the Copa America is wonderful but gives no guarantees of success in the World Cup qualifiers, Uruguay coach Oscar Tabarez said after his team's record triumph on Sunday.
"This is very gratifying, very nice, but a qualifying series is something else because it's not played at one venue, where presumably the only ones with an advantage are the home team," Tabarez said.
"To have won the Copa America has no bearing on the qualifiers, it's no guarantee."
The South American qualifiers, a nine-nation, 18-round series spanning two years, are just around the corner, kicking off in October. Tabarez, in charge for five years, has built a team that has put Uruguay back on the map. "We have to have faith in our things, we prepared for the (Copa America), we did it well," said Tabarez.