Westley was sacked by Preston in February, just over 12 months after leaving Stevenage for Deepdale, but returned with a 1-0 win as Max Ehmer, on loan from QPR, struck in the 76th minute at Broadhall Way.
Defeat left Pools eight points adrift of safety with only four games remaining.
Pools' Charlie Wyke tested Steve Arnold after 10 minutes, holding off Boro skipper Mark Roberts before squeezing in a right-footed effort on the turn.
Quick feet from Dani Lopez saw the Spaniard skip past Neil Austin but his deep cross was headed straight at Scott Flinders by James Dunne before the break.
Roberts then met Dunne's corner at the back post, but the 29-year-old could not guide his header on target after 55 minutes.
Ehmer broke the deadlock with 14 minutes to go, latching onto Freeman's deflected effort inside the area to coolly slot past Flinders in the Pools goal.
Moments later Luke Freeman nearly doubled the home side's lead, but the ex-Arsenal winger's effort was tipped away by Flinders.