Uche broke free in the area in the 10th minute and was brought down by goalkeeper Keylor Navas, who was shown a direct red card.
Villarreal team captain and midfielder Bruno Soriano stroked in the penalty kick after Javi Jimenez replaced Navas.
Jimenez kept Levante in the match until Soriano delivered a through ball for Uche to score in the 74th. The Nigeria international scored again with a bicycle kick in the 89th.
Garcia drew a foul from Rayo goalkeeper Ruben Martinez who was sent off with a red card in the 25th.
Garcia converted the penalty kick and then added a second goal for Espanyol from the spot in the 51st when striker Jonathan Cordoba was fouled by Anaitz Arbilla.
Saul Niguez gave Rayo some hope with a headed goal in the 81st. But Garcia managed to toe the ball home while falling backwards to seal the win two minutes later. Substitute Christian Stuani hit on the break in the 85th to cap Espanyol's much-needed victory.
"It's impossible to take the ball from Rayo," said Espanyol coach Javier Aguirre. "It always has more possession than its rivals, even Barcelona and Real Madrid. We tried to maintain our composure and take advantage of the chances their errors provided us, and early on that's what we got with Sergio Garcia and Cordoba. If we had pressed Rayo early they would have run over us."
Sevilla forward Carlos Bacca scored one goal and set up another at Sanchez Pizjuan Stadium to keep Betis winless on the road this season and stuck in last place.
Bacca struck two minutes in from a touch pass by Jose Antonio Reyes to set the tone, and Sevilla's defense dogged Betis up and down the pitch from start to finish.
Betis lost defender Paulao when he was booked for a second time in the 42nd for fouling Reyes, and Stephane M'bia headed the resulting free kick served by Ivan Rakitic through the hands of goalie Sara Guillermo.
After Betis again lost the ball in its half, Bacca chipped a pass to Victor "Vitolo" Machin to beat Sara from a tight angle in the 65th.
Vicente Iborra, who had hit the post earlier, completed the demolition in the 88th with a header to turn in Rakitic's corner kick.
"We knew that as hosts we had to go at them," Bacca said after his first game against Sevilla's crosstown rival. "The derbies are like finals, you don't play them, you win them. All week when I was out, at a restaurant eating with my family, people stopped to tell me how important this game was."
Valencia outplayed Elche in the first half but could go no closer than Jonas' shot off the crossbar from close range six minutes in.
Fidel Chaves put Elche in front in the 57th with a well-directed header to flick Edu Abacar's pass off the base of the far upright and into the net.
Valencia pushed Elche into its area and Juan Bernat banged in his own rebound in the 73rd after goalkeeper Manuel Herrera parried his initial volley.
Cristian Herrera went on in the 79th and five minutes later took Ferran Corominas' pass lobbed into the area and beat 'keeper Diego Alves with a shot from the left elbow of the six-yard box to claim the three points.
Elche's win lifted it level on points with Valencia in the middle of the table.
On Saturday, leader Barcelona didn't miss the injured Lionel Messi as it eased past Granada 4-0 to maintain its three-point advantage over Atletico Madrid, which demolished Getafe 7-0.
Also, Real Madrid lost Cristiano Ronaldo to a hamstring injury after he scored in a 5-0 win at Almeria, while Carlos Vela scored four goals to give Real Sociedad a 4-3 win over Celta Vigo.
Athletic Bilbao hosts Malaga on Monday.
