Veteran striker Beckford slotted home his sixth goal in 10 games to extend North End’s unbeaten league run to 12 games, with the victory moving them seven points clear of third-placed Swindon.
Preston started well and had a great chance to take the lead after 14 minutes but Callum Robinson’s left-footed effort from 18 yards was pushed away by Josh Lillis.
Rochdale had the ball in the net on the half-hour mark, but Ashley Eastham’s header was ruled out for offside.
And Preston took the lead after 36 minutes when Beckford gathered from a Scott Laird throw-in and fired a right-footed strike under Lillis from eight yards.
Ian Henderson headed over the bar shortly after half-time for Dale before League One’s top scorer Joe Garner stooped to plant a header just wide for the hosts.
Garner came close again with another header late on but his effort was well saved by Lillis’.