Beckford opened the scoring from the penalty spot in the 38th minute and wrapped up the points for Simon Grayson's men with a second 10 minutes after the break.
Colchester could have had a 16th-minute penalty when Lubo Michalik appeared to pull Phil Ifil's shirt but the offence went unpunished. And the response from referee Andy Woolmer was the same three minutes later when Kevin Lisbie went down under another Michalik challenge.
In fact, it was Leeds who were to take the lead from the spot when former Leeds defender Matt Heath brought down Becchio and Beckford fired into the bottom-left corner from 12 yards.
Beckford pounced again in the 55th minute. Jonny Howson chested down a high ball from Robert Snodgrass and shot against the far post, with Beckford forcing in the rebound.
The striker was denied his hat-trick by a 64th-minute offside flag before Leeds defender Leigh Bromby headed against the bar late on.