The Azulones are without a league win since November and play host to fellow strugglers Granada lying just two places and one point above the drop zone.
That miserable run - they have picked up just four points from a possible 36 since their last victory and lost to rock-bottom Real Betis last weekend - led to the dismissal of manager Luis Garcia on Monday, with former Romania international Contra immediately installed as his replacement.
Gavilan has been impressed with what he has seen from the former Getafe, AC Milan and Atletico Madrid defender, and said the players are with the new boss "to the death".
However, the forward also stressed how vital the supporters will be in the battle against the drop.
He said: "The fans are perhaps almost the most important part. We want them to score the first goal and to get behind us, because we are going to respond.
"These first three points against Granada will allow us to face the remainder of the season with much more confidence.
"Maybe it's the most important game of the season up to now and we want that response from the fans. The team are going to give their all and we are going to be united from the first minute to the last."
Contra will need to hit the ground running in his new role as, after Granada, they face a daunting run of fixtures which sees them take on top-eight sides Athletic Bilbao, Villarreal, Valencia and Atletico Madrid in the space of five games.
He has made a good first impression, though, with Gavilan saying: "The feelings are all positives, everything's very good.
"I'm not going to get into comparing now to before, we are with the coach to the death and the only objective is Granada.
"Right now we are in a critical situation and we have to give it our all."
Granada are three points better off than Getafe thanks to their 2-0 win over Villarreal last time out.
The Andalusian side have only scored eight times away from home this season - the joint-worst record in the division - but they have still managed to pick up four victories, and they are hoping to notch another on Friday.
Forward Piti said: "It's a very important game for us to distance ourselves from the relegation zone. We cannot think about anything else, our minds can only be on getting the three points on Friday."