Coutinho, dressed in a black shirt dotted with white stars, was in the stands at the Camp Nou for the first time since his 160 million-euro ($192 million) move from Liverpool.
It didn't take long for the Brazilian star to appreciate the playing riches on show on the pitch.
"The first half was extraordinary," said Barca coach Ernesto Valverde.
Level at 1-1 after the first leg, the three-time defending champions were 4-0 up by half-time.
Messi then returned the favour by setting up Alba to score past the hapless Sergio Alvarez in the Celta goal before Luis Suarez made it 4-0 on the night after 30 minutes when the Uruguayan burst through the defence.
The tie petered out in the second half but French international Ousmane Dembele showed why Barcelona paid 105 million euros for him last year when he dribbled past three defenders from the halfway line before being denied by a desperate tackle.
"It's luxury to have Leo in the side, he's the best in history. We always look for each other to score goals and today we have done it twice," said Alba.
Earlier Thursday, Espanyol overturned a 2-1 loss in the first leg to defeat Levante 2-0 with Leo Baptistao and Gerard Moreno on target either side of half-time.
Sevilla also progressed with a 2-1 win at home to second-tier Cadiz for a 4-1 aggregate.
On Wednesday, Real Madrid laboured to a 2-2 draw with Numancia to progress to the quarter-finals 5-2 on aggregate.
In a much-changed side, Lucas Vazquez scored both of Real's goals after the 11th and 59th minutes.
But on both occasions, their modest visitors fought back thanks to a brace from Guillermo on the stroke of half-time and then after 82 minutes.
Numancia ended the game with 10 men after captain Dani Calvo was red-carded in the dying moments.
Leganes, a modest club from the Madrid suburbs, reached the quarter-finals for the first time in their 89-year existence.
Moroccan international Nabil El Zhar scored the crucial away goal for mid-table Leganes on the half-hour mark.
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
