However, Frankie de Jong's dismissal for a second booking proved a turning point. With an extra man, Espanyol drove forward in search of an equaliser and got their reward when Lei fired past Neto in the 88th minute to become the first Chinese player to ever score against Barca.
Barca were miles off the pace in the first half but roared back after the break, with goals from Suarez and Vidal showing their ability to win games when not necessarily playing well. That good work, though, was eventually undone.
On Suarez and Vidal, they're so often Barca's saviours when it's not Lionel Messi. Suarez has either scored (six) or assisted (four) their last 10 league goals, while midfielders Vidal has netted six goals in the league despite only playing 570 minutes.
Dropped points are becoming a theme on the road for Barcelona this season. If they can't turn around their away form -- and performances -- then the league title could slip away from them. They remain top, but this draw means they now only lead Real Madrid, who beat Getafe earlier in the day, by goal difference.
The midfield was to blame as much as anyone here. Ivan Rakitic was really bad in the first half but it's De Jong who will cop the majority of the criticism. He's been consistently good since signing from Ajax but was at fault for Espanyol's first goal and his dismissal went on to cost Barca two points.
Manager rating out of 10
4 -- Ernesto Valverde seems unable to improve his team's performances away from Camp Nou. That has to be a real concern. He looked to have adjusted things here by bringing Vidal on at the break but was unable to set his 10 men up to hold on to three points.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Neto, 5 -- The Brazilian made his first league appearance for the club due to an injury to Marc-Andre ter Stegen. The first goal was not his fault but questions will be asked about Lei's winner. Would Ter Stegen have saved it?
DF Gerard Pique, 6 -- Cleaned up a couple of mistakes from his teammates in the opening stages but was part of a Barca backline that conceded twice (Lopez was unmarked for the first goal) and looked out of sorts in the latter stages of the game.
DF Clement Lenglet, 5 -- Struggled against Espanyol's pressing early on and could have done better with his positioning to prevent Lei's winner.
DF Jordi Alba, 6 -- Has had a hard time finding form this season and that continued in the first half. There were finally signs of life after the break, though, including the assist -- his first of the season -- for Suarez's leveller.
MF Sergio Busquets, 5 -- The only midfielder who started the game to last the 90 minutes. That was because Rakitic was so poor and De Jong was sent off, though, more than anything else.
MF Frenkie de Jong, 4 -- A rare off night and his worst game in a Barcelona shirt. Gave away the free kick which led to the Espanyol goal and was sent off for a second booking after giving the ball away in the middle of the pitch.
MF Ivan Rakitic, 4 -- Scuffed a shot from the edge of the box and then gave the ball away cheaply in his own half. And that was just the first four minutes of the game. Didn't improve and was hooked at half-time.
FW Lionel Messi, 6 -- Wasn't involved in any of the goals but had his moments. Saw three tame first half efforts saved by Diego Lopez in the first half. Almost produced an amazing assist after the break, but Suarez shot straight at the keeper after Messi had beaten five men and fed his teammate with a clever reverse pass.
FW Luis Suarez, 7 -- Infuriates supporters for large parts of games but is still consistently delivering match-changing moments. Hit the post in the first half before scoring the equaliser and expertly setting up Vidal for the second. Missed chances to seal the three points, though.
FW Antoine Griezmann, 5 -- Linked with Messi a couple of times in the first half but all in all this was another quiet performance from the Frenchman.
MF Arturo Vidal, 7 -- Changed the game after coming on at the start of the second period. Scored the winning goal but was also played a part in the first, with his run drawing the centre-backs away from Suarez.
DF Nelson Semedo, NR -- Came on for Griezmann after De Jong was dismissed to help balance the side.