That set a new record record of 39 fixtures unbeaten in the competition (across this season and the end of last), but Barca have lost on their two previous visits to Celta in the Primera Division.
Here, Goal takes a look at everything you need to know ahead of Tuesday's clash at Balaidos...
Ivan Rakitic is still suffering from a broken finger and will miss out, along with long-term absentee Sergi Samper. Lucas Digne is doubtful.
Valverde has no players suspended for the trip to Galicia.
Barcelona potential starting line-up
With Rakitic out, Paulinho should keep his place alongside Sergio Busquets in central midfield, with Philippe Coutinho and Ousmane Dembele set to be included and Andres Iniesta rested.
In defence, Thomas Vermaelen looks likely to come in to give Gerard Pique a rest, while Nelson Semedo is set to start ahead of Sergi Roberto at right back.
Lionel Messi and Luis Suarez will be paired together in attack.
Celta Vigo team news
Celta Vigo thrashed Sevilla 4-0 in their last home game, but this has been something of an inconsistent campaign for the Galician side, currently in ninth place with 43 points.
Juan Carlos Unzue's side drew 2-2 at Camp Nou earlier this season and are five points behind sixth-placed Villarreal, giving them an outside chance of securing a spot in the Europa League next season.
Hugo Mallo and Pablo Hernandez miss out through suspension on Tuesday.
TV channel & kick-off time
Celta versus Barcelona kicks off at 21:00 local time on Tuesday and will be broadcast live in the UK (United Kingdom) on Sky Sports Football from 19:55 BST.
In the United States, the game can be watched live on television on beIN SPORTS and kicks off at 15:00 ET.
Best Opta match facts
Since the start of the 2014-15 season, Celta have beaten Barcelona three times in La Liga, which is more than any other club in the competition.
Celta have won the teams' last two league meetings at Balaidos, scoring eight goals in those games (a 4-1 win in 2015-16 and a 4-3 victory last term).
Lionel Messi has four goals and five assists in his last four appearances against Celta.
Iago Aspas has four goals and two assists in his last four games against Barcelona.
Philippe Coutinho has racked up four assists in his last three league games for Barca, having managed only one in the previous nine.