Cucinotta held off Giorgia Bronzini (Wiggle Honda) for the stage honours at Dukhan Beach with her Ale Cipollini team-mate Marta Tagliaferro third.
The victory gives Cucinotta the race lead and a four second advantage over Bronzini.
"In the final the all the girls were there to do the lead out and, and at 500m to go Chloe (Hosking) was pulling with Jolien (D'hoore) in her wheel," said Bronzini.
"I tried to go out next to the barriers but I had no space enough so I must go around one rider and do my sprint. But Cucinotta came from the back really fast! She is fast!
"I'm a little bit disappointed that we didn't get the victory, because everybody worked really hard for me. But it was a great job from the team because it was the first time that we have raced together!"
The 98km stage lacked the infamous Qatari wind, leaving it to be a bunch sprint after Xiu Jie Jiang (Chongming-Liv-Champion System) forged the day's only breakaway.
Shelley Olds beat Chloe Hosking (Wiggle Honda) in the first intermediate sprint and finished second behind Jiang in the second sprint, her effort elevating her to third overall.
Stage 1: 98.5km, Museaum of Islamic Art - Dukhan Beach
1 Annalisa Cucinotta (ITA) Ale Cipollini 2hr 28min 36sec
2 Giorgia Bronzini (ITA) Wiggle Honda
3 Marta Tagliaferro (ITA) Ale Cipollini
4 Lucinda Brand (NED) Rabo Liv Women
5 Shelley Olds-Evans (USA) Bigla
6 Trixi Worrack (GER) Velocio-SRAM
7 Arianna Fidanza (ITA) Ale Cipollini
8 Jolien D'hoore (BEL) Wiggle Honda
9 Kelly Druyts (BEL) Topsport Vlaanderen -Pro-Duo
10 Tiffany Cromwell (AUS) Velocio-SRAM
1 Annalisa Cucinotta (ITA) Ale Cipollini 2hr 28min 26sec
2 Giorgia Bronzini (ITA) Wiggle Honda 0:00:04
3 Shelley Olds-Evans (USA) Bigla 0:00:05
4 Marta Tagliaferro (ITA) Ale Cipollini 0:00:06
5 Elisabeth Armitstead (GBR) Boels Dolmans 0:00:08
6 Chloe Hosking (AUS) Wiggle Honda
7 Lucinda Brand (NED) Rabo Liv Women 0:00:10
8 Trixi Worrack (GER) Velocio-SRAM
9 Arianna Fidanza (ITA) Ale Cipollini
10 Jolien D'hoore (BEL) Wiggle Honda