Bookwalter, Martin Elmiger (IAM Pro Cycling) and Gregory Rast (Radioshack Leopard) slipped the peloton with 11 km to go just as the front of the race was reforming after being sliced into pieces in the desert crosswinds.
The trio rapidly gained 30 seconds, saw its lead peak at 45 seconds and barely held off the chase by the Omega Pharma-Quick Step team in the final kilometres of the 145.2 km stage.
Bookwalter said he was hoping his breakaway companions would start sprinting farther out.
"But they left it really late – they're both smart, really strong riders," he said. "But I was able to tuck in just for a second and get around them. I had been telling myself (in the final kilometers) that I was going to win, but it was a shock to see my wheel go over that line first. It was a feeling I haven't had in a really long time so it was really special and exciting."
Bookwalter's win was his second of a six-year professional career, adding to his victory in the prologue of the 2009 Tour of Utah. The Albuquerque native donned the race leader's golden jersey and also earned the silver points jersey of the six-day race that continues Monday with a 14km team time trial.
"We looked at the course yesterday and it's a pretty typical, Qatar affair," Bookwalter said. "It will be windy and there's a couple corners and turnarounds but we have a really good team for it. Today, the guys were really strong and I think we'll show that again tomorrow."
Elmiger edged Rast for second, while Team Sky’s Austrian rider Bernhard Eisel finished fourth after outsprinting former stablemate Mark Cavendish (Omega Pharma-Quick Step) and fifth-placed Italian Elia Viviani (Cannondale).