"He's an extraordinary player. Spectacular. A natural leader. It's a blessing to have him with us, it's marvellous.
"He's a model, a born worker. He's humble, he works for the team, he helps the coaching staff, he makes the difference."
Barca jumped up to second on seven points from three matches, two behind Real Betis. Real Madrid will attempt to maintain their perfect start to the season at Espanyol later on Sunday.
Xavi handed Kounde his first start after the club was finally able to register the France defender they signed from Sevilla last month for a reported 50 million euros ($49.8 mn).
After a goalless draw on the opening weekend, Barca put four past Real Sociedad last time out, and the Catalans began in similar fashion with Lewandowski going close with an early header.
Lewandowski met an in-swinging delivery from Raphinha, his glancing effort striking the post and rebounding off Valladolid goalkeeper Jordi Masip before tricking along the line to safety.
Pedri then spotted the run of Raphinha in behind but the Brazilian was thwarted by Masip, who was well beaten moments later when Ousmane Dembele's venomous shot clipped the crossbar.
Barca's pressure finally told as Raphinha whipped in another teasing cross, sowing confusion in the Valladolid defence which a gambling Lewandowski punished by stabbing home.
A marauding Dembele tested Masip from range, and then created the second for Pedri by rolling a perfectly-weighted ball for the midfielder to bury with a first-time side-foot finish.
Lewandowski all but put the game beyond reach on 64 minutes, running onto a pass from Dembele and cleverly backheeling past Masip with the help of a deflection off Joaquin Fernandez.
Valladolid nearly pulled one back but Marc-Andre ter Stegen saved well from Oscar Plano and Kounde stuck out a leg on the line to keep out the follow-up effort from Roque Mesa.
Ansu Fati forced a sharp stop from Masip after coming off the bench, but Barca grabbed a fourth in stoppage time as Roberto volleyed home after Lewandowski was denied a hat-trick after Masip tipped his shot onto the bar.
Villarreal dropped their first points of the season in a 0-0 draw at Getafe as Unai Emery's side saw the award of a penalty overturned following a VAR review in the dying stages.