Messi, already Barcelona's top scorer of all time, became La Liga's leading marksman on Saturday as his hat-trick helped the Catalan giants to a 5-1 win over Sevilla.
The Argentina star has now netted 253 top-flight goals in Spain, as he eclipsed the tally set by legendary Athletic Bilbao forward Telmo Zarra almost 60 years ago.
The Sevilla victory was Barca's third in a row in all competitions, though Luis Enrique's side remain two points behind leaders and rivals Real Madrid.
Away successes at Ajax and Almeria followed disappointing consecutive defeats to Real and Celta Vigo, and Luis Enrique's men appear to be back on track ahead of their trip to Cyprus for the Group F fixture.
Midfielder Xavi is confident his side will only to continue to improve after Saturday's emphatic showing.
"We played a great game," Xavi is quoted as telling AS.
"We have seen a great Barca - a very complete performance. We certainly enjoyed playing our football.
"We've seen the best Barca of the season and the best Messi. We have to continue on this path. We have to continue improving.
"There are 25 players and we're all compatible. The coach is responsible for picking who plays but we're all compatible."
Neymar and Ivan Rakitic also scored for Barca, but all the attention was on Messi - who coach Luis Enrique described as a "unique" talent.
Andres Iniesta and Jeremy Mathieu (calf) are both in doubt for Barca, while the match will come too soon for Thomas Vermaelen despite the ex-Arsenal man returning to training after hamstring and thigh issues.
Barca sit second in Group F, one point adrift of Paris Saint-Germain, but are assured of their progression to the last 16.
As long as they do not lose to APOEL, they can overtake PSG when they meet in the French capital on December 10.
If APOEL do not lose, they can finish ahead of Ajax and in third - which brings with it involvement in the UEFA Europa League - if they beat the Dutch champions next month.
APOEL have taken just one point in their four pool matches, but are in far better form domestically and lead the league.
They remained unbeaten in the Cypriot top flight with a goalless draw at second-placed Apollon on Friday, giving them their fourth clean sheet in a row in the league.
APOEL, who have only conceded twice in 10 matches, are already eight points ahead of Anorthosis, who sit third.
Barcelona could only edge past APOEL on matchday one, with Gerard Pique's 28th-minute goal giving them a 1-0 win in the only previous meeting between the two sides.
