Wood retired the side to preserve the Cubs' 4-1 Cactus League win over the Angels, needing just seven pitches to end the game.
"Woody's making [the decision] easier, not tougher," Cubs manager Lou Piniella said. "Let's wait on that decision. But he's making it easy."
The last test for the right-hander to clinch the closer's job is to show he can pitch on consecutive days. That will happen this week.
"Obviously, they need to see if I can do it, and it's important to know if I can do it," Wood said. "For me, it's just another day to come in and get ready to go."
All three closer candidates got their work in Sunday. Bob Howry, who has an ugly 11.81 ERA in six games this spring, pitched two innings in the Minor League camp. Carlos Marmol was in the Cubs-Angels game, and served up a first-pitch home run to Erick Aybar in the seventh inning. Marmol laughed about it after the game. He played with Aybar in the Dominican Republic.
"It was a fastball," Marmol said. "[Aybar] already told me, 'Give me a fastball.'"
The right-hander has had trouble with command of his fastball but felt Sunday was better.
"That was my best day," Marmol said. "I'll take this day."
He struck out the next batter after Aybar, then gave up a single to Kendry Morales before getting a double play as Bobby Wilson struck out and Morales was caught stealing. As for the closer's job, Marmol says he'll take whatever assignment he gets.
"Whatever decision they make will be fine for me," he said.
Would he like to close?
"Yeah," Marmol said, smiling. "Why not?"
Wood hasn't lobbied for the job, except when he takes the mound.
"Whatever happens, I'm just glad to be healthy and part of a, hopefully, winning team, and I hope to have a chance to do it in the postseason," he said. "I honestly don't put too much thought in [winning the job]. I think we have a great bullpen and guys who know how to pitch."
The only issue regarding Wood is durability. Can his shoulder stand up to a closer's workload?
"He's been throwing strikes, he's been going after the hitters, his velocity has been good, he's mixing in nice hard sliders," Piniella said. "He's really been throwing well this spring. We just want to see him back to back."
On Friday, Wood needed just six pitches -- all strikes -- to retire the side in order. On Sunday, he threw one ball out of his seven pitches. He got a big assist from Mike Fontenot, starting at shortstop, who was able to get to a grounder that Piniella thought was a potential base hit. It was an impressive end to the game.
"I just feel better," Wood said. "The ball's coming out better. Not so much during the game, but I've had command warming up of my slider and fastball. A couple years ago, I felt OK and my velocity was there but the location was off. I've been able to throw strikes and I feel good."
He's hitting 95-98 mph on the radar gun with his pitches, and isn't spending extra time in the trainer's room. Those are all good signs for Wood. Carlos Zambrano picked up the win on Sunday and looked sharp. Does Big Z have a preference as to who his closer is on March 31?
"Either way, I don't care," Zambrano said. "Whoever closes the game for us, I know all three guys can do the job -- Marmol, Howry and Woody. I'm happy with whatever Lou says."
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.