The 1-0 home win on Friday (Saturday AEDT) gave the hosts a boost in the 10-team round-robin competition after a long losing streak.
Miguel Araujo scored the only goal of the match with a header in the 88th minute to move Peru out of last place in the South American standings.
Third-placed Uruguay have 15 points after nine matches, four less than leaders Argentina and one behind second-placed Colombia.
The first six teams in the table will secure a berth in the next World Cup in 2026 in North America.
Peru have six points, one more than last-placed Chile.
Uruguay wasted several opportunities in the first half, with Federico Valverde, Darwin Nunez and Maximiliano Araujo stopped by Peru goalkeeper Pedro Gallese.
The hosts took control of the match in the second half.
"I honestly feel responsible, due to the players we had in the midfield and in the offence, for such a small proportion of goal chances we created in the second half," Uruguay coach Bielsa said after the match.
Uruguay will host Ecuador on Tuesday, the same day that Peru face fourth-placed Brazil.
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