Both teams will face Group B members; those teams will be decided Tuesday night.
Suarez, Uruguay's most dangerous striker all day, ran unguarded to the back post and headed in Edinson Cavani's brilliant cross for his first goal of the tournament.
The two countries went into the last group game sharing the lead at four points and needed only a draw to advance. But both fielded attacking lineups. Even so, the game yielded few clear scoring chances.
Uruguay, which didn't allow a goal in the first round, ended the group phase with seven points after overpowering South Africa 3-0 and drawing 0-0 with France.
Mexico earned four.
