Reserve-team manager Bowyer and youth boss McPhillips took up the reins when Henning Berg was sacked after 57 days and 10 games at the helm last week.
Under their guidance, Blackburn recorded a 3-1 weekend win at Barnsley before despatching Nottingham Forest 3-0 on New Year's Day - the club's first back-to-back Championship victories since October.
A statement on Blackburn's official website read: "This decision follows discussions between the owners, directors and global advisor (Shebby Singh).
"The club would like to take this opportunity to thank Gary, Terry and the rest of the staff for their sterling efforts over recent days which have helped produce two successive and important league victories.
"The club's search for a new permanent manager will continue in earnest."
Following Saturday's FA Cup third-round tie with Bristol City, Blackburn's January programme features Championship trips to Wolves and Brighton either side of hosting Charlton.
They lie 13th in the table, five points shy of the play-off places despite the departures of Berg and predecessor Steve Kean this season.