Monaco, whose ranking has plummeted to 105 after a series of injuries going back to late 2013, recovered from breaks down in both sets to claim victory over Dutch seventh seed Haase, a losing finalist here a year ago to Mikhail Youzhny.
It will be a first-ever meeting for Monaco in the final against world number 71 Andujar, who profited from seven double-faults off the racquet of fourth seed Fernando Verdasco in a 6-3, 6-7 (2/7), 6-1 upset.
Verdasco, treated for a shoulder problem after losing the opening set, broke in the second set as his opponent served for a straight-sets win.
Verdasco then stayed alive by claiming the second set in a tiebreak before collapsing in the third to exit as his serve was broken seven times.
Earlier, the 30-year-old Monaco went through to his first final since Kitzbuehel 51 weeks ago after playing his first semi-final of 2014.
The South American has been bothered by three different injuries this season -- his back, wrist and foot.
His victory took his 2014 record to 13-14 and 5-1 at this alpine village whose clay stands 1,050m above sea level.