Taggart was 24 of 37 for 334 yards and three TDs, and had 63 yards and a TD on 18 carries.
Ricky Otis finished with 11 tackles to lead the Crusaders’ defense, which held Fordham scoreless in the second half.
The Rams (1-10, 0-3 Patriot League) led 21-14 at halftime, before Taggart and Eddie Hougton scored two touchdowns each.
Masella, a former New York City firefighter who came to Fordham after coaching at Central Connecticut, was 27-40 in six years at the Bronx-base school.
Taggart hit Kyle Toulouse on a 71-yard pass midway through the third quarter to tie it, before running for a 6-yard TD with 10:01 to play. Houghton then had TDs of 38 and 3 yards.
Houghton finished with 153 yards on 15 carries for Holy Cross (6-5, 4-2).
Ryan Higgins had 238 yards and two touchdowns on 23 of 41 passing for the Rams.