Rodwell, who has not played since sustaining an ankle injury in the 1-0 defeat to Aston Villa on August 29, played 54 minutes at the club's Finch Farm training ground before being substituted.
Watching manager David Moyes now has to decide whether the 19-year-old is ready to face the Seasiders again for the first team on Saturday.
Anichebe, who has not played since the final day of last season after being sidelined by a knee injury, replaced Beckford for the last 20 minutes and set up the second of Jose Baxter's two goals.
Baxter initially opened the scoring, with Magaye Gueye and Beckford making it 3-0.
Baxter's second was followed by a late strike by substitute Hope Akpan.