He was drafted in the first round of the 1979 NFL Draft by the Chargers and played for them until 1987, when he retired from football due to injury. After a knee injury prematurely ended his rookie season, Winslow, as part of Air Coryell, led the NFL in receptions in 1980 and 1981, becoming the first tight end ever to lead the league in receptions in back to back seasons. He also exceeded the 1,000 yards receiving milestone in 3 different seasons, including setting an NFL single season record for receiving yards by a tight end with 1,290 yards in the 1980 season. The record stood until Rob Gronkowski totaled 1,327 in 2011. In a 1981 regular season game, Winslow tied an NFL record by catching five touchdown passes.
In a 1981–82 playoff game against the Miami Dolphins that became known as The Epic in Miami, Winslow caught a playoff record 13 passes for 166 yards and a touchdown, while also blocking a field goal with seconds remaining to send the game to overtime in one of the greatest single player efforts in NFL history. Winslow's yardage total stood as the playoff record for tight ends for 30 years until Vernon Davis's 180 yards in 2012. What made Winslow's performance all the more memorable was that fact during the game he was treated for a pinched nerve in his shoulder, dehydration, severe cramps, and received three stitches in his lower lip. After the game, a picture of Winslow being helped off the field by his teammates became an enduring image in NFL Lore.
Tight ends prior to Winslow were primarily blockers lined up next to an offensive lineman and ran short to medium drag routes. Winslow was put in motion so he would not be jammed at the line, or he was lined up wide or in the slot against a smaller cornerback. Former Chargers assistant coach Al Saunders said Winslow was "a wide receiver in an offensive lineman's body." Chargers head coach Don Coryell said, "If we're asking Kellen to block a defensive end and not catch passes, I'm not a very good coach Back then, defenses would cover Winslow with a strong safety or a linebacker, as zone defenses were not as popular. Strong safeties in those times were almost like another linebacker, a run defender who could not cover a tight end as fast as Winslow. Providing another defender to help the strong safety opened up other holes. Former head coach Jon Gruden called Winslow the first "joker" in the NFL. He could line up unpredictably in any formation from a three-point stance as a blocker to a two-point stance or being in motion as a receiver. Head coach Bill Belichick notes that the pass-catching tight ends who get paid the most money are "all direct descendants of Kellen Winslow" and that there are fewer tight ends now who can block on the line.
Winslow's son, Kellen Winslow II, also plays tight end in the NFL. Winslow II was drafted in the first round of the 2004 NFL Draft from the Miami Hurricanes by the Cleveland Browns, the team the Chargers traded with to draft the elder Winslow in 1979. He wore his father's jersey No. 80 when he played for the Cleveland Browns, as a sign of respect for his accomplishments.