The 28-year-old left a terrible impression as his debut - after completing a six-month loan move from Real Betis in January - came in front of the home fans.
With the host trailing by 2-0, Boudebouz was shown a straight red for a harsh challenge on Borja Mayoral in the 49th minute.
His expulsion compounded his team's woes as they conceded two more goals but Brais Méndez's effort from the penalty spot reduced the deficit in the 88th minute.
49' Boudebouz levanta la pierna en la entrada a Mayoral e impacta con los tacos en la pierna del jugador rival. #CeltaLevante— RC Celta (@RCCelta) February 16, 2019
The Algerian midfielder is now set to miss the next two matches as Celta Vigo chase their second league win since the start of the new year.
Morocco’s Sofiane Boufal was on parade for the full duration on the losing side while Nigeria's Moses Simon, Cote d'Ivoire's Cheick Doukoure and Ghana's Raphael Dwamena were all in action for Levante.
The defeat dropped Celta to 16th in the LaLiga table with a point off relegation zone while Levante climbed to 11th with 30 points 24 matches.