Promoted Valladolid hadn't won in the first five games of the Spanish top-flight season, despite only conceding five goals.
Sergio Postigo scored on the rebound after his header was saved by goalkeeper Josep Masip to put Levante in front in the 47th minute.
The match swung in the hosts' favor after Enes Unai leveled with a header in the 50th.
Levante midfielder Nikola Vukcevic was then sent off after receiving a second yellow card for elbowing a player in the head.
Defender Nacho Martinez completed the turnaround in the 56th when he volleyed in a corner from outside the penalty area.
"We played a very good match, a complete match," Valladolid coach Sergio Gonzalez said. "Their goal hurt us, but we responded and fought back. In our previous matches we had done many things well and this victory backs that up."
Valladolid is 13th in the 20-team standings with six points, while Levante is 17th on four points.
ALAVES IN TOP 4
A stoppage-time goal from Jonathan Calleri earned Alaves a 1-1 home draw with Getafe, extending a surprising start to the season that has lifted the modest Basque club into fourth place.
Alaves had won three in a row and hasn't lost since its opening match.
Getafe went in front with a goal by Amath Ndiaye in the 80th minute, after goalkeeper David Soria had saved a penalty by Alaves' Ibai Gomez late in the first half.
BETIS WINS AWAY
Real Betis secured its first away win of the season with a 1-0 victory at Girona.
Lorenzo Moron scored midway through the second half before Betis goalkeeper Pau Lopez saved Christian Stuani's powerful header in injury time.