The 22-year-old Argentine World Player of the Year, who netted a hat-trick against Valencia at the weekend, scored twice and helped create another as Barca romped to a 4-0 victory which sealed a 5-1 aggregate success.
NEWS:More Messi magic mauls Stuttgart
"Jam session at the Nou Camp," columnist Ramon Besa wrote in Spain's El Pais daily.
"Messi plays as if he were a seasoned jazz musician, always recognisable but different every night," he added.
"He improvises with the same old score, the band follows him and he plays with a religious faith, and the fans demand that the music never stops."
Writing in La Razon daily, Luis Buxeres noted that Messi's stunning recent form, which has brought him eight goals in his last four matches in all competitions, had coincided with a switch to a more central role.
"The right wing is no longer his domain and he now operates with complete freedom behind the striker," Buxeres wrote. "And the team is grateful for it."
The German media were also effusive in their praise for Messi, the Frankfurter Rundschau pointing out the huge gulf in class between the Spanish and European champions and their hapless visitors.
"Barcelona and their superstar Lionel Messi were several ticks too good for VfB Stuttgart," the paper said. "The Swabians got a football lesson on Wednesday at the Nou Camp."
Germany's Bild daily focused on how Messi had helped end the European career of Stuttgart's 40-year-old goalkeeper Jens Lehmann, a former Germany number one.
"Messi fires Lehmann into Euro retirement," the paper wrote. "The Swabians could only keep Barcelona at bay for 13 minutes. Then Leo Messi let rip - and how!"
Fernando Llamas summed Messi's performance up in Spanish daily El Mundo: "With a soloist like Messi any obstacles in the way are flattened. Just give him the ball."
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