Bishop is attempting to become the first goalie in Stars/Minnesota North Stars history to achieve the feat and the first in the NHL since Brian Boucher of the then-Phoenix Coyotes had five consecutive shutouts from Dec. 31, 2003 to Jan. 8, 2004.
Bishop has allowed one goal on 124 shots (.992 save percentage) in his past four starts.
The Stars, 5-1-0 in their past six games, hold the first wild card into the Stanley Cup Playoffs from the Western Conference, two points ahead of the Arizona Coyotes, three ahead of the Wild and two points behind the St. Louis Blues for third place in the Central Division.
Dallas has a game in hand on Arizona and Minnesota, which has lost two straight and is 1-2-2 in its past five.