Top ranked Novak Djokovic, looking for his fourth Dubai title, had a much easier time against good friend Viktor Troicki, beating him 6-1, 6-4 in just over an hour.
Del Potro, who reached the quarterfinals in Marseille and won his 14th title the week before in Rotterdam, appeared sluggish early, handing the first set to Baghdatis when he hit one of his three double faults. But the 2009 U.S. Open champion served better in the second, and broke Baghdatis to go up 3-2. The two traded breaks in the third and Del Potro won it when the Cypriot hit a forehand into the net after a short rally.
Del Potro then saved three match points at 5-4 in the third before forcing the tiebreaker.
"I was fighting every time of the match," Del Potro said. "He's a great player. He fights like me every point, and we made fantastic rallies. The crowd was enjoying the game. I'm so glad to beat him tonight in Dubai."
Del Potro said his right wrist is still bothering him, having missed most of 2010 after having surgery on it and still struggling to return to the top.
"I'm trying to keep focus on this tournament because it's very important," Del Potro said. "And then to come for Indian Wells and Miami, I need good results here."
Tsonga, who had never lost in six meetings against Llodra, blamed the loss partly on the fact he only arrived in Dubai on Monday after winning the Open 13 in France. Tsonga also said a key turning point was when he had to replay a point at 4-3 in the first set, double-faulted twice and was broken.
"Maybe if I win the first set it gives me enough energy, maybe to play in the second and maybe win," Tsonga said. "But after that, I'm just disappointed and then I'm scared. ... I was supposed to win this set, and you do like two double faults because you're thinking about it. That's it."
Llodra broke Tsonga twice in the second set to go up 5-2 and clinched the match when his fellow Frenchman hit a return long.
"Today I didn't start well," Llodra said. "Beginning of the second set, I break him early, and after, it was just to be focused on my serve. ... It's special to beat him."
Coming off his third consecutive Australian Open title, Djokovic broke the 44th-ranked Troicki twice to easily win the first set. The second was tighter, with Troicki breaking Djokovic to even the set at 4-4. But Djokovic broke back and then clinched the match with a slicing serve that Troicki couldn't return.
"That was a great one, especially in the first set, considering the fact I haven't played an official tournament for three, four weeks," said Djokovic, who now has a 13-1 record against Troicki. "This is one of the fastest hard courts on the tour that I have experienced outdoors. So you need to be really committed to every point and play well."
In other matches, sixth-ranked Tomas Berdych made easy work of American wild-card entry Rajeev Ram, beating him 6-1, 6-3. Australian Bernard Tomic withdrew from his match against Romanian Victor Hanescu after falling behind 3-2 in the first set.
Former third-ranked Nikolay Davydenko of Russia had the other upset on the day, downing ninth-ranked Janko Tipsarevic 6-0, 7-5. It was the third tournament in a row that the Serb had lost his opening match after he injured his heel at the Australian Open.
The big-hitting Tipsarevic had trouble with his serve all match, committing six double faults and finishing with a first serve percentage of only 49 percent.
The 46th-ranked Davydenko said it was clear Tipsarevic isn't playing at this best.
"Maybe he doesn't have the confidence after the Australian Open," the Russian said. "After his injury, he tried to come back. (His) game is good but is not enough now. Maybe he will feel better in America."