Mancuso opened the scoring with a 4-yard run in the opening quarter and capped the Spiders' scoring with a run from the 3 in the final seconds of the third quarter.
The Spiders have won 14 straight home openers since 2005.
Mancuso guided a Richmond offense that amassed 476 total yards - including 320 on the ground and 156 passing.
Maurice Jackson scored a 56-yrd TD off a fumble when Colby Ritten sacked Jacksonville's Calvin Turner Jr. Aaron Dykes and Milan Howard also scored rushing TDs for Richmond.
The Dolphins Craige Saxton threw one pass, a 71-yard touchdown to Jordan Younge-Humphrey. Turner completed four of eight passes for 65 yards, and rushed for 32 more with a TD.
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