Gerrard, who has won this award (six) more times than any other player, scored four times last month, including two penalties to help his side memorably defeat Manchester United 3-0 at Old Trafford.
Suarez, meanwhile, wins his second monthly award of the season after scoring six goals in March, including a superb hat-trick in the 6-3 victory over Cardiff City.
The award has been awarded jointly to two players on only five previous occasions, the most recent coming in April 2007 when Tottenham strikers Dimitar Berbatov and Robbie Keane shared the spoils.
Rodgers has claimed the manager's award after leading Liverpool to five victories in the month of March - a run which has seen them climb to the top of the Premier League.
The Northern Irishman masterminded wins over Manchester United, Cardiff City, Southampton, Tottenham and Sunderland, with his team scoring 18 goals in the process.