Earlier Atletico Madrid eased to a 2-0 win over Las Palmas and moved third, with coach Diego Simeone's son Giuliano netting his first goal for the club.
With second-place Real Madrid not in action after their game at Valencia was called off because of the devastating floods in the region, Hansi Flick's soaring Barcelona stretched their lead on the champions.
Raphinha netted in between Olmo's goals as Barcelona racked up a three-goal lead by the 31st minute at the Olympic stadium.
Javi Puado pulled one back as Espanyol fought hard to avoid a derby pummelling in the second half, with the visitors scoring three disallowed goals.
"I'm not happy about the second half... we lost concentration, lost tension, in tennis you say unforced errors, but it happens sometimes," admitted Flick.
"Today I accept that because we won, but for Wednesday (in Europe) we need another level."
Barcelona have started life under Flick in sensational form and after beating Bayern Munich and Real Madrid last week, earned their 10th win in 11 La Liga matches.
"I'm back, enjoying it, playing, winning, and I want more," Olmo told DAZN after his first start since mid-September.
Barca's marquee summer signing produced an electric display in the first half.
"He knows how to score goals, this was very important for us today," Flick told reporters.
"This is also why we won this match, and these important three points."
Teenage Spain star Lamine Yamal crafted his first goal with a delicious pass using the outside of his boot, which Olmo dispatched with an explosive finish.
Brazilian winger Raphinha lofted the second over Garcia when Marc Casado produced a fine pass which split Espanyol's defence.
Olmo added his second with a powerful low drive but after that Barcelona were frustrated as neighbours Espanyol, 17th, battled well.
After two Espanyol strikes were rules out for offside, Puado found the net and then had another goal ruled out as the ball had gone out of play.
Injured Barcelona winger Ferran Torres, from Foios in the Valencia region, wrote in a post on Instagram that he did not have the strength to come to the stadium to watch the game because of the impact of the floods.
"I totally understand that, it was normal," said Flick, who suggested on Saturday the whole round of fixtures should have been postponed.
"There are things that are more important than football, he chose that and it's normal."
Simeone success
Atletico coach Diego Simeone had said there was "no sense" in playing La Liga matches this weekend because of the floods, but his team secured a comfortable victory.
Donations of food and other useful products were collected outside the Metropolitano stadium in support of those affected in the east of Spain by the floods which have killed more than 200 people.
"I'm very happy for my first goal for Atletico but we can't ignore everything that's happening in Valencia, all the victims there. I send my support and strength to them," said Giuliano Simeone.
The hosts took the lead after 37 minutes when Nahuel Molina's long ball found Simeone darting in behind the defence.
The striker, deployed on the right wing by his father, burst into the box and swept the ball into the far corner.
"Giuliano I see as a football player," said Diego Simeone.
"From the first moment that we decided he would stay with us (in the squad) this season, it's with the intention that he can help us."
The coach explained that his son's workrate was a key factor in him starting.
"He has a responsibility and not a name, I look at it that way... those who run most, play, and those who don't, play less," said the Argentine.
