The visitors, now coached by Javi Gracia following the sacking of Jose Luis Mendilibar earlier this month, had plenty of chances over 90 minutes and took the lead through Roberto Torres after 11 minutes.
But Getafe hit back to take their first win of the season thanks to Miku's brace either side of the interval.
Osasuna kept pushing right to the death and were unlucky not to take at least point from the game after Oriol Riera struck the bar inside the final five minutes.
The visitors went ahead with their first attack of the match, Emiliano Armenteros providing a cross from the left wing for Torres who arrived on cue to turn the ball home from 12 yards.
After three straight defeat it marked a perfect start for Gracia, who led Almeria to promotion to the top flight last season before his contract ended.
Juan Valera almost levelled for the hosts in the 25th minute when he headed wide from six yard, but Getafe's opener did arrive 10 minutes later when Miku headed in Pedro Leon's corner.
Miku almost made it two a minutes before the break when he struck the post from close range, as Getafe ended the half on the front foot.
The hosts maintained their momentum after the restart and took the lead in the 52nd minute when Diego Castro picked out Miku and the Venezuela striker did the rest with a cool finish into the bottom-right corner.
Osasuna pushed hard for an equaliser in what time remained with Riera rattling the bar late on with a fine effort from the edge of the area, before Damia's long-range effort was kept out by Miguel Moya.
And moments later Moya was in action again, this time turning away Lolo's effort from an Armenteros free-kick as Getafe held on for victory.