Nelson, a restricted free agent prior to re-signing, played in all 16 games last season. He added four tackles on special teams.
The 28-year-old has spent time with the Chargers and Redskins prior to signing with the 49ers in 2014.
Celek had two catches for 53 yards in an injury-plagued 2014 season. He signed a one-year deal. Nelson got a four-year contract.
Both players were listed as questionable on the team's final injury report, though it was reported early Saturday that Gore would in fact suit up for the game. Crabtree has yet to miss a game this season.
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