He began his career as a starter but was converted to a reliever by 1976. He was promoted to AAA Tidewater in 1977 where he posted 14 saves with a 2.64 ERA going 11-6 as well. He made the 1978 Mets pitching staff out of Spring Training under manager Joe Torre.
Cornejo debuted at Shea Stadium on April 8th 1978, in the Mets third game of the year. He came in relief in the 7th inning with the Mets down 5-2 to the Montreal Expos. The Mets rallied winning the game with a classic Ed Kranepool walk off pinch hit HR, giving Cornejo his first career win. The next day he earned a save. He would get another win a week later as Lenny Randel provided an extra inning game winning hit in Montreal. He picked up another win against the Chicago Cubs & was 3-0.
A couple of bad outings followed, including a five run one inning performance against the Big Red Machine on April 29th where Pete Rose homered off him. He pitched better in May earning a save & two holds but was still sent down to Tidewater at the end of the month. He returned in September, earning another save & one final victory also coming against the Expos. He finished the year at 4-2 with three saves & a 2.45 ERA in 25 appearances. He struck out 17 but walked 14 in 36 innings.
At the end of the year he was traded to the Detroit Tigers for Queens born, Ed Glynn. After one year with Tigers minor leagues, Cornejo retired. His son Nate Cornejo pitched for the Detroit Tigers from 2001-2004 going 12-29 with a 5.41 ERA in 56 games.