Espanyol had looked on course to claim their own maiden victory after establishing a 2-0 lead inside the opening 25 minutes through fine efforts from summer signings Samuele Longo and Sergio Tejera.
However, Levante hit back at the start of the second half to draw level with quickfire goals from Juanlu and Christian Lell and then, despite losing striker Vicente Iborra to an 82nd-minute red card, the home side snatched the points when Michel's cross was deflected in three minutes into stoppage time.
Despite taking only one point from their opening two league games, Levante came into Sunday's match buoyed by Thursday's victory over Motherwell which saw them qualify for the group stage of the Europa League on their continental debut.
It was Espanyol who enjoyed the much better start on Sunday, though, and they took a 21st-minute lead when 20-year-old Longo, who joined on loan from Inter Milan this week, smashed in a stunning volley from inside the area.
Four minutes later it was 2-0 as Tejera, who switched from Real Mallorca this summer, produced a superb curling left-footed finish to beat Levante goalkeeper Gustavo Munua from 25 yards out.
At that stage it looked as though Espanyol would be celebrating their first win of the season.
Levante had other ideas, though.
With a strike that even outshone Espanyol's two goals, Juanlu halved the deficit in the 54th minute when he lashed an unstoppable 25-yard drive into the top corner after a Jose Barkero corner had been laid back to him.
The home side's fans had barely finished celebrating that goal when Levante drew level when Lell slotted home at the second attempt.
Levante were favourites to find a winner after that, but their hopes took a major hit in the 82nd minute when Iborra, having been booked earlier in the half, was shown a second yellow for a foul on Juan Forlin.
But despite being reduced to 10 men, Levante still sought a winner and Ruben Garcia and Bakero tried their luck before the hosts claimed the victory right at the death when Michel's low cross took a deflection off Espanyol defender Raul Rodriguez which left his keeper Cristian Alvarez wrong-footed.