NEW YORK (CNN) -- New York Housing Authority supervisor Felix Vasquez admitted Thursday he was scared when a frightened mother threw her three-week-old son from a burning third-floor Bronx apartment -- right into his arms.

"The mom was panicking," Vasquez told CNN's "American Morning." "A lot of smoke in the apartment, she was nervous. She said, 'It's either me or my baby.' She let the baby go, and, thank God, I was there at the right time."

Vasquez said he didn't have time to think. The baby -- not breathing -- landed upside down in his waiting arms, and he whisked him away and "gave him mouth-to-mouth." (Watch Felix Vasquez make the catch of his life as he saves the baby -- 1:38)

"It started crying," he said. "... and the fire department came over and did their part."

"Their part" included rescuing the mother.

"She's doing great," Vasquez said of the mother. "She took a lot of smoke in, but she's doing excellent."

"She came up to me, hugged me, kissed me and kept thanking me and thanking me."

Vasquez is the catcher for the Housing Authority baseball team -- which has won its division three years in a row.

The rescuer gave the baby mouth-to-mouth resuscitation -- a skill he picked up as a teenage lifeguard.

Tracinda Foxe, 30, was cornered by smoke and flames in the Bronx apartment on Wednesday when she went to the window with son Eric Guzman, The Associated Press reported.

"God, please save my son,"' Foxe told the Daily News in Thursday editions, according to the AP. "I prayed that someone would catch him and save his life."

Moments after the catch, the AP said, firefighters D.J. Martin and Bobby Eustace burst into the burning apartment, found a hysterical Foxe and gave her an oxygen mask.

The New York Fire Department said the call about the fire came in about 8:22 a.m. Wednesday. The cause, fire officials said, was still under investigation but appeared to be the result of careless cooking.