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The Eagles were 22-8 down at half-time as Dewsbury took control thanks to scores from Luke Adamson, Dalton Grant, Etu Uaisele and Aaron Brown, Mark Mexico and Yere crossing for the hosts.
And the visitors extended their lead to 28-8 early in the second half courtesy of Nathan Conroy.
However, Sheffield hit back with five tries of their own. Rob Worrincy got two and Quentin Laulu-Togagae and Keal Carlile also touched down before Yere grabbed his second try late on to earn the Eagles just their fifth win of the season.
Stage 7, Vasto - L'Aquila (185km)