Neal's three-goal performance was the second of his career. Malkin's five-point night gave the NHL's leading scorer 93 points for the season.
Pascal Dupuis also scored for Pittsburgh, which crept to within one point of the New York Rangers atop the Eastern Conference standings with the victory.
Brad Thiessen earned the win with 26 saves.
Bryan Little notched two goals for the Jets, who remained four points out of the eighth and final playoff spot in the East.
Ondrej Pavelec started in net for Winnipeg but was yanked after yielding five goals on 24 shots.
Chris Mason relieved and allowed three goals on 11 shots.