Halep looked to be going the distance in Doha on Thursday only to storm back in a second-set tie-break and record a 7-6 (7-1) 7-6 (8-6) victory.
The French Open champion, who will rise to second in the new WTA rankings next Monday, trailed 4-1 in the second breaker of a tense battle and saved two set points before eventually moving into the last four.
Halep, playing her first tournament with Thierry Van Cleemput as her coach, will take on Elina Svitolina after overcoming the powerful German.
Former world number one Halep lost just three points in as many games to open up a 4-0 lead, with her opponent struggling to get going.
Georges, already with a title under her belt this year after her success in Auckland, eventually warmed to the task, unleashing a barrage of ferocious forehand winners to break three times and force a tie-break.
The composed Halep got back into her stride in the breaker, however, a majestic backhand winner down the line seeing her go 4-1 up as she reeled off five successive points to take the set.
Halep struck the first blow in the second, an early break helping her move 3-1 ahead, but it was back on serve when the favourite was broken to love to be pegged back at 5-5.
An aggressive Georges punched the air after winning a pulsating rally with a brilliant volley at full stretch, yet the battling Halep fended off two set points and put away a forehand volley to seal victory at the first attempt.