In other matches, Ecuador trounced Panama 4-0 with two goals from Fidel Martinez in Guayaquil, while Radamel Falcao scored the winner in Colombia’s 1-0 victory over Costa Rica in Buenos Aires.
Paraguay and Honduras drew 2-2 in Asuncion, with former Manchester City striker Roque Santa Cruz getting both Paraguay’s goals.
While Suarez was helping Barcelona win the Champions league title in Berlin, his young understudy Diego Rolan put Uruguay one up after four minutes from Alvaro Pereira’s cross.
Edinson Cavani then added a brace, his first a tap-in after Rolan had hit the post, then a penalty on the half-hour to put the home side 3-0 up at half-time.
Substitutes Giorgian De Arrascaeta and Abel Hernandez increased Uruguay’s lead before Guatemala pulled one back through defender Wilson Lalin 12 minutes from time.
The Uruguayans open their defence of the Copa America title against Jamaica on June 13 and also meet Argentina and Paraguay in Group B.
Suarez is serving a ban of nine international matches in competition after biting Italy’s Giorgio Chiellini at the World Cup.
Despite missing Lionel Messi, Javier Mascherano and Carlos Tevez, all of whom played in the Champions League final, Argentina found it just as easy against Bolivia.
Di Maria had the opener after 24 minutes with an angled drive from the edge of the box. Aguero got his first four minutes later with a penalty kick and then added another on the half-hour when he clipped home a cross at the near post.
Di Maria slotted home from the spot at 54 minutes and Aguero sealed his hat-trick a minute later.
Ecuador, who are Chile’s opponents in the tournament’s opening match in Santiago on Friday, also ran up a 3-0 lead in the first half against Panama.
Striker Miller Bolanos scored the first from a pass by tricky winger Jefferson Montero after he had beaten two defenders in the box in the 26th minute.
Martinez then scored twice in eight minutes, first from Montero’s pass then with a header from left back Walter Ayovi’s cross.
Seven minutes into the second half, Montero added the fourth for Ecuador, who also meet Mexico and Bolivia in their Copa group.
Colombia captain Falcao settled a more even affair at the Diego Armando Maradona ground in the Argentine capital in the opening minute of the second half, scoring from Juan Cuadrado’s low cross.
(Additional reporting by Alexandra Valencia in Quito, Luis Ampero in Buenos Aires and Daniela Desantis in Asuncion; Writing by Rex Gowar; Editing by Ian Ransom)