Randolph also said that Tom Glavine, Orlando Hernandez, Oliver Perez and John Maine would be the team's other starters to open the season. No order has been established.
Pelfrey said he had no real pangs on Sunday that he might have blown this opportunity, despite the forgettable performance against the Astros.
"It didn't go as well as I'd like," he said after giving up six hits and a walk on 84 pitches. "I still feel like I'm getting better. I still feel like I made some progress."
Pelfrey was particularly upset about a changeup he threw to former Yankee Mike Lamb in the third inning with two runners on. The pitch stayed high, and Lamb drove it to right-center for two runs.
"That is something to learn from," Pelfrey said. "I didn't execute. I know there will be days like this where you want to take back two or three pitches."
The competition for the fifth spot had been thinning out before Sunday, with Phil Humber demoted, Chan Ho Park charted for bullpen work and Aaron Sele likely facing a similar fate.
Still, Pelfrey's mother, Anna, helped him resist an urge to feel smug about his chances.
"Nothing is guaranteed," she kept telling him. Pelfrey called his mother a "pretty tough lady" who helps keep him grounded.
Before he heard from Randolph, Pelfrey had said, "They haven't told me anything. I'm just going to keep going about my business and doing the best I can."
Meanwhile, Maine, who will be the third or fourth starter, also can smile now after an overall strong spring, despite the fact that he was touched for 12 hits and four runs in 5 2/3 innings on Saturday in a split-squad game against the Marlins.
Maine's biggest satisfaction on Saturday came from knowing that he kept the Mets in the game. It was 4-4 when he left.
"It was one of those days," Maine said. "They were beating me to death with singles. They found a lot of holes. At least I can say I kept the game close."
Maine only walked one and struck out five. He is expected to get one more start before the regular season commences April 1.
It was suggested to the right-hander that he should be allowed to have an off game every now and then.
"Hopefully it is only once in a blue moon," Maine said, smiling.