Getafe parted company with Luis Garcia on Monday following a 12-game winless run in La Liga but Contra was unable to provide the perfect tonic in a game that saw both teams reduced to 10 men.
And yet the hosts led at the break after goals from Ciprian Marica and Lisandro Lopez eclipsed Riki's leveller.
Youssef El-Arabi, who had set up Riki, equalised twice after the interval, with Angel Lafita on target for Getafe in a thrilling encounter.
Contra saw his charges make a superb start as Marica raced away from Manuel Iturra's challenge before lifting a cool finish over Roberto with just six minutes gone.
El-Arabi played in Riki to score the equaliser against his former club 10 minutes before the break, but Getafe responded within three minutes through Lopez.
Granda were back on level terms after 62 minutes through El-Arabi, but then Iturra saw red and Lafita restored the home side's advantage.
Despite the numerical disadvantage, the visitors hit back once again with El-Arabi's 77th-minute strike, before Sergio Escudero was dismissed for Getafe.
The draw extends Granada's winless run on the road to six matches, while Contra's side are just two points above the relegation zone.
