Dos Santos finally netted his maiden goal for Mexico, opening the scoring at Levi's Stadium in his 40th appearance for his nation.
In Gerardo Martino's second game in charge, Mexico claimed their victory on the back of a strong start, with a Gustavo Gomez own goal and Javier Hernandez strike following Dos Santos' opener.
Hernan Perez pulled a goal back for Paraguay in the second half before substitute Miguel Almiron's red card, and Derlis Gonzalez's effort gave them some hope.
However, Luis Montes sealed Mexico's win in additional time.
After a victory over Chile, Martino opted for changes – making 10 in total to his starting line-up.
But it seemed to have no impact on Mexico as they made a dream start, scoring twice in the opening nine minutes.
Dos Santos opened the scoring after Edson Alvarez – the only player backing up for Mexico – tried to pick out Hernandez, a Paraguayan defender's clearance falling for the LA Galaxy man to volley in smartly from close range.
Paraguay produced some more poor defending to fall 2-0 behind through a Gomez own goal.
Hernandez fed a pass to Erick Gutierrez on the left side of the area and his cross was turned in by Gomez.
Just as Paraguay looked for a way back into the contest, Hernandez scored his 51st international goal to extend Mexico's lead.
Gutierrez found Dos Santos, whose first-time pass released Hernandez to finish clinically in a one-on-one with Antony Silva.
It should have been 4-0 in the 53rd minute, but Gutierrez struck the post with an effort from near the penalty spot after a cross from the right.
Instead, Paraguay pulled a goal back through Perez, who drilled in a pass from Oscar Romero just before the hour-mark for his second international strike.
However, their chances of an incredible comeback were dealt a blow when Newcastle United midfielder Almiron was sent off seven minutes after coming on for a poor challenge on Jose Juan Vazquez.
Paraguay found a second goal when Gonzalez struck from inside the area in the 84th minute after a poor turnover deep in defence, but Montes sealed Mexico's win following an Alexis Vega flick-on, although the goal should have been ruled out for offside.
What does it mean? Martino's Mexico making quick progress
While a win over Chile in Martino's first game in charge was impressive, the first-half display against Paraguay was even more so. Mexico were clinical and looked dangerous, but unlike during their victory over Chile, they appeared in control for longer periods.
Dos Santos grabs chance
Dos Santos is yet to shine for Mexico, but he took a major step on Tuesday. The 28-year-old scored his first international goal and also set up Hernandez's strike with a nice pass in a performance sure to keep him in Martino's plans.
Rough start for Berizzo
Starting something of a rebuild of Paraguay, former Sevilla coach Eduardo Berizzo suffered defeats in his first two games in charge. However, Matias Rojas was handed a starting debut, while the likes of Santiago Arzamendia and Carlos Gonzalez were also in the XI and picked up their first international caps. Pleasingly for Berizzo, Paraguay continued to fight, although their efforts defensively would have been a worry.
Mexico look to continue their strong start under Martino when they face Venezuela and Ecuador in June, while Paraguay are not scheduled to be in action until the Copa America, although they may opt for at least one friendly before the tournament starts.