From 14 meters, Espericueta tapped in a cross from Alberto Acosta, rolling his shot inside the near post as Tigres moved into first place in Group 6, one point ahead of Alajuelense.
Tigres has one game remaining, at home on October 24 against Alajuelense. The Costa Rican side will play Esteli at home next week.
Needing a win to remain alive, Real Esteli struck first in the 53rd minute as Juan Barrera rose above two Tigres defenders and powerfully headed in Franklin Lopez's corner kick from the edge of the six-yard box.
Tigres had two chances to equalize one minute apart after the hour mark, but Alan Pulido's shot after dancing along the end line was easily parried away by Justo Lorente in the 65th minute.
One minute later, Fernando Navarro was unable to tee up a shot inside the box.
Two minutes after dangerously coming off his line and missing an attempted punch, Lorente's best save came in the 73rd minute when he made a diving stab to his right to thwart Taufic Guarch's open header inside the box.
Esteli appeared destined to survive, but Espericueta dashed those hopes, silencing Estadio Independencia.
The Mexican visitors attacked from the outset, threatening twice inside the opening five minutes. But Francisco Acuna's 35-meter blast skimmed the post and two minutes later David Toledo hammered a shot over the bar from top of the 18-yard box.
Real Esteli had its first quality scoring chance in the 17th minute, but Gabriel Mirazo's side-volley following a corner kick sailed well over the bar.
Two minutes later, Lorente had to parry the ball over the net to avoid an own-goal as an attempted clearance nearly turned catastrophic.
In the 33rd, Tigres keeper Jorge Diaz De Leon had to dive to his right to save Ronald Jaramillo's header inside the box.
The match was in stark contrast to the clubs' first meeting at Estadio Universitario on August 1, when Tigres won 4-0 with four different players scoring in the final 55 minutes.