Burawa was called up from Triple-A Scranton-Wilkes Barre prior to Sunday's game against the Detroit Tigers and sent back down following the Yankees' 12-4 loss.
The 26-year-old righty reliever -- a Long Island native, drafted out of St. John's -- gave up four runs in 2/3 of an inning in relief of Masahiro Tanaka, including J.D. Martinez's third home run of the game.
Lefty Jose De Paula, 27, who replaced Burawa and also was making his major league debut, gave up one run in 3 1/3 innings of mop-up duty and was sent back down to Triple-A after the game too.
In their places, the Yankees plan to call up a pair of righties prior to Monday's series opener against the Philadelphia Phillies: 27-year-old Diego Moreno and 23-year-old Nick Rumbelow.
Moreno, acquired from the Pittsburgh Pirates in the A.J. Burnett trade back in 2012, is 3-0 with a 2.27 ERA and one save in 19 appearances at Triple-A this season, giving up 26 hits in 35 2/3 innings.
Rumbelow, a seventh-round draft pick out of LSU in 2013, is 2-1 with a 3.31 ERA and seven saves in 25 appearances at Triple-A this season, and has struck out 41 batters in 35 1/3 innings.
The Yankees also plan to transfer injured reliever Sergio Santos from the 15-day disabled list to the 60-day DL. Santos will be having Tommy John surgery in the coming days.