Sharpe's three TDs gave him 61 for his career, surpassing Jerry Smith's record for career scores by a tight end. It was his first three-touchdown game since Oct. 6, 1996 against the Chargers.
Sharpe, already the all-time leader in catches and yards by a tight end, finished with seven receptions for 101 yards.
While Plummer went 23-of-34 for 253 yards, San Diego's Doug Flutie completed just 9-of-25 passes for 70 yards, one TD and an interception.
Flutie, who accounted for four touchdowns in last week's win over Minnesota, also lost three fumbles.