During an 8-year playing career, primarily as a catcher, he played from 1979 to 1987 for three major league teams. During a 7-year managing career, he managed from 2001 to 2007 for the Texas Rangers and the Cincinnati Reds. Narron was the third base coach for Israel at the 2017 World Baseball Classic.
Narron was born in Goldsboro, North Carolina. He is a Christian Zionist. His father John was employed as a salesman and floor layer for the Isaacs-Kahn Furniture Company in Goldsboro. He is a nephew of former major league catcher Sam Narron.
Through his childhood he played baseball at the Wayne County Boys Club, and attended Goldsboro High School where he played baseball, basketball, and football, and graduated in 1974. He went to college at East Carolina University.
Narron played in the major leagues for eight seasons with three different teams: the New York Yankees (1979), Seattle Mariners (1980-81, 1987), and California Angels (1983-86).
He was drafted out of high school in the sixth round by the New York Yankees in the 1974 Major League Baseball Draft. He played alongside brother Johnny for the Johnson City Cardinals in the Rookie Appalachian League during his first professional season in 1974, batting .301. In 1977, playing for the West Haven Yankees of the AA Eastern League, he batted .299 (8th best in the league) with 28 home runs (2nd in the league) and 93 RBIs (3rd in the league) in 438 at bats.
He made his Major League debut on April 13, 1979. Narron played for the Yankees as the backup catcher to Thurman Munson, who died in a plane crash in August 1979. He was the Yankees' starting catcher the day after Munson's death, and remained in the dugout during the pregame ceremonies, leaving the catcher's position empty, out of respect for Munson.
In November 1979 Narron was traded by the Yankees to the Seattle Mariners with Juan Beniquez, Rick Anderson, and Jim Beattie for Jim Lewis and Ruppert Jones.
He was released by the Mariners in March 1982, and signed two days later as a free agent by the California Angels, for whom he played. Playing for the Spokane Indians in the AAA Pacific Coast League (PCL) in 1982, he batted .311 in 408 at bats. In 1983, playing for the Edmonton Trappers of the PCL, he batted .301 with 27 home runs (4th in the league) and 102 RBIs (6th in the league) in 539 at bats, while leading the league with 15 intentional walks. He was released by the Angels in April 1987, and signed later that month by the Seattle Mariners, who in turn released him the following November. He retired as a player in 1989.
Narron was a manager in the Baltimore Orioles farm system from 1989 through 1992; of the Class A Frederick Keys (1989), AA Hagerstown Suns (1990-91), and AAA Rochester Red Wings (1992), with a record of 291-269 (.520). He was then hired as a coach for the Orioles by skipper Johnny Oates. After two seasons in Baltimore, he moved with Oates to the Texas Rangers.
Narron was third-base coach for the Rangers from 1995 until he was named Interim Manager May 4, 2001, after the firing of manager Johnny Oates. He had the interim tag removed and managed the team during the 2002 campaign. He was replaced in Texas by Buck Showalter in December 2002. In 1995, when the Rangers opened their season after the strike which canceled the World Series the previous year, it was at Yankee Stadium. The first game back from the strike held special significance for Narron since it reminded him of the day after Thurman Munson died and he was the Yankees' starting catcher for the first game after that tragedy, which was also played at the old Yankee Stadium. On this particular day after the baseball strike ended, Narron was the Rangers' 3rd-base coach.
Narron then served as bench coach for the Boston Red Sox during their 2003 run to the ALCS, and performed the same role for Cincinnati in 2004–05.
Narron was named as the Reds' Interim Manager on June 20, 2005. On September 29 of that year, his contract was extended to cover the 2006 season with a mutual option for 2007. Narron was fired as manager of the Reds on July 1, 2007. The Reds named advance scout Pete Mackanin as the interim manager. Narron's record with the Reds was 157–179.
On February 25, 2008, Narron was named a special assignments scout and front-office consultant with the Rangers.
Narron served as bench coach for the Milwaukee Brewers from 2011-15.
Narron was hired to be the 2017 manager of the Reno Aces on December 30, 2016.
After the first seven games of the 2017 season, Narron took over as interim bench coach of the major league Arizona Diamondbacks, when bench coach Ron Gardenhire left the team on a leave of absence to have and recover from prostate cancer surgery.
Narron was the third base coach for Israel at the 2017 World Baseball Classic qualifier. Narron, whose daughter Callie lives in the Arnona neighborhood of Jerusalem, Israel, with her husband (Devin Mitchell) and two children (Aviel and Lydia), said: "I love the game, I love the Jewish people and I love Israel".
Narron is married to Donna Narron. He has seven children, five of his own Callie, Caitlyn, Clare, Cara, and Connor and two stepchildren, Hunter and Chelsy. Connor was the fourth-ranked prospect for the high school class of 2010 by ESPN's Perfect Game. The Orioles selected Connor in the fifth round of the Major League Baseball Amateur draft. Narron's brother, Johnny was the hitting coach for the Milwaukee Brewers from 2012-14. Narron is the nephew of former Major League catcher and coach Sam W. Narron, and cousin of pitcher Sam F. Narron.