Entering the 1944 Brooklyn Dodgers season, Webber remained the team's primary relief pitcher, leading the team again with 48 appearances throughout the season. His best outing of the year came on July 19 against the Cincinnati Reds, which saw him allow two hits and no runs over  innings in a 10–5 win.
Entering the 1944 Brooklyn Dodgers season, Webber continued to serve as the team's main backup pitcher, leading the team once more with 48 appearances throughout the year. His most successful performance of the season occurred on July 19 against the Cincinnati Reds, in which he allowed two hits and no runs over several innings in a 10–5 victory.