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Atletico were stunned early on at the Jose Zorrilla after Oscar Plano fired Valladolid into the lead before half-time.
However, the newly-crowned champions of Spain rallied back in the second half as Angel Correa pulled back an equaliser before Suarez slammed home Atletico's second of the match.
Los Blancos defeated Villarreal 2-1 at the Alfredo Di Stefano Stadium, but Atletico's 2-1 win over Valladolid moved them two points clear at the top of La Liga.
Suarez arrived at Atletico last September after Barcelona boss Ronald Koeman told the Uruguayan striker he wasn't part of his plans at the Camp Nou.
The 34-year-old ex-Barcelona star's move provided additional firepower to Atletico's frontline as they secured the league title for the first time since 2014.
Footage has since emerged of an emotional Suarez on the pitch after the match as the Atletico striker couldn't hold back the tears.
Suarez scored an impressive 21 times in La Liga this season, finishing behind Gerard Moreno, Karim Benzema and top scorer Lionel Messi.
The Uruguay international, whose current Atletico deal will expire next summer, made 38 appearances across all competitions this season.
Suarez's departure from Barcelona after six years was heavily criticised by former teammate Messi, who insisted that he 'deserved' better treatment.
Messi posted on Instagram last September: "You deserved a farewell that fit with who you are: one of the most important players in the history of the club.
"Someone who achieved great things for the team and on an individual level.
"You did not deserve for them to throw you out like they did. But the truth is that at this stage nothing surprises me anymore."
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