Iago Aspas gave the home side the lead on 24 minutes and although that goal was soon cancelled out by Odion Ighalo, Mario Bermejo grabbed the winner nine minutes from the end.
Resino was named as Paco Herrera's successor on Monday and inherited a club in the relegation zone, four points from safety and without a win in their last six league games.
And although they remain in the bottom three, today's three points means they are now just two behind Real Zaragoza in 17th.
Granada boss Lucas Alcaraz, whose side are only three points above Celta, had warned that the home side would be extra motivated with a new man at the helm and that proved to be the case.
The home side created the first chance after five minutes and Granada goalkeeper Antonio Tono was forced into a double save from Augusto Fernandez's shot and Fabian Orellana's follow-up header.
It was therefore no surprise when Celta took the lead, Aspas lobbing the ball into the bottom corner from six yards out.
But the lead lasted barely three minutes as Ighalo volleyed home from 12 yards to level the scores.
Alex Lopez then fired over from long range as action switched quickly to the other end, before Gabriel Torje failed to get a header on target for Granada from close range.
Chances were hard to come by in the second half but Ighalo was unlucky not to grab his second of the game just before the hour, seeing his thumping drive from the edge of the area come back off the bar.
And Celta rubbed salt into the wound 20 minutes later as Bermejo's mishit shot found the back of the net from 12 yards to seal a vital victory.