A cyclist pedaling a $4,000 racing bike at high speed through Central Park slammed into a suburban mom in town shopping for her daughter’s birthday present — leaving the woman brain-dead, sources said.

Jill Tarlov, 59, of Fairfield, Conn., the wife of a CBS executive, was in a crosswalk near 63rd Street when Jason Marshall, 31, came barreling along West Drive at around 4:30 p.m. and yelled for her to get out of his way, law enforcement sources said.

Tarlov was rushed to New York-Presbyterian Hospital/Weill Cornell Medical Center, where she was declared brain-dead, the sources said.

Tarlov, whose husband, Michael Wittman, is a senior vice president at CBS, was out shopping for her daughter’s present when she was tragically struck, sources said.

Marshall, an accomplished baritone saxophone player, was pedaling a pricey Jamis Eclipse racing bike when he spotted the woman in the crosswalk at an intersection controlled by a traffic light, sources said.

“He was riding in the car lane and yelling, ‘Get out of the way! Get out of the way!’ ” one source said.

It was unclear who had the light, but Marshall — who remained at the scene — “admits to being in the wrong lane,” the source added.

Marshall was at the Central Park Precinct station house Thursday night and cops were talking to the Manhattan DA’s Office about possible charges.

Law enforcement sources said it’s common for athletic cyclists to pedal in the car lanes, enabling them to travel faster.

“These guys think that they have entitlement and they don’t ride in the bike lanes,” one source said.

Witness Phillip Fenton, 21, visiting New York on a geography field trip from England’s University of Exeter, said Marshall was “speeding,” adding, “It didn’t look like he tried to stop.

“He was yelling for her to get out of the way, but I don’t think she heard him,” Fenton added.

Fenton’s pal Tom Longman said Marshall was hunched over the brakeless, triathlon-style “aerobars” attached to the handlebars of his high-performance, yellow and black ride.

“She went down pretty hard,” Longman said. “The right side of her face looked very bad. There was blood all over her.”

Local residents have long complained at Central Park Precinct Community Council meetings that the cyclists are a danger.

Last month, a 75-year-old Brooklyn Technical HS physics teacher was killed in Central Park when a cyclist trying to avoid a pedicab slammed into him.

Irving Schachter was struck in the park Aug. 3 and died two days later at New York-Presbyterian Hospital.