I couldn't find a rookie Marlins that played for the Phillies that has the record for most saves as a rookie. However, Dontrelle Willis in his rookie season had 14 wins, a Marlins team record for a rookie. He is currently on the Phillies.
Ted Williams, with 145 RBIs in his rookie year, holds the record.
Frank Tanana in 1974.
Tony Esposito, who holds the modern era record for most shutouts in a season (15), achieved his shutout record as a rookie. Though he had played 13 games the season previous, he was still considered a rookie and won the Calder Trophy, the NHL's rookie of the year award.
WR Keenan Allen has set the Chargers rookie record for most receptions in a season. Thru week 14 of the 2013 NFL season he has made 61 receptions. The previous record holder was WR John Jefferson who caught 56 passes in his rookie season in 1978.
Eric Dickerson of the 1983 Los Angeles Rams with 1808.