Jimenez suffered a 1-0 defeat at Racing Santander in his first game in charge last weekend but it looked set to be a better outing for him as his side took a 38th-minute lead through Maurizio Lanzaro and still held that advantage heading into the closing stages.
However, with 11 minutes to go, Zaragoza defender Javier Paredes inadvertently put through his own net to help Getafe salvage a 1-1 draw.
The result leaves Zaragoza rooted to the foot of the standings but it at least brought an end to their six-match losing streak in La Liga, while Getafe remain just above the relegation dogfight.
The home side were the first to threaten with Adam Pinter bringing a parry out of visiting goalkeeper Miguel Moya in the 11th minute, but Getafe were quick to respond with Dani Guiza testing Zaragoza custodian Roberto Jimenez.
Guiza was then denied by a brilliant save from Roberto in the 37th minute and Zaragoza made the most of that escape as they raced down the other end to take the lead after winning a corner.
Luis Garcia curled in the flag-kick and Lanzaro got on the end of it to power an unstoppable header past Moya.
That goal separated the two sides at the break, although Zaragoza were again indebted to Roberto for keeping them in front as he performed more heroics to keep out Javi Casquero's 44th-minute shot.
Roberto was enjoying a fine night and he prevented Abdelaziz Barrada drawing Getafe level on the hour with another top-class stop.
The former Atletico Madrid and Benfica custodian was finally beaten in the 79th minute though as Getafe grabbed a late leveller.
Pedro Leon curled in a corner from the left and Parades turned the ball into his own net.
Both sides had chances to take the points in the closing stages but Roberto turned away Leon's shot and Moya kept out a Lanzaro header as the spoils were shared.