Article updated 27/01/2014
The Reds forward, who agreed a one-month loan deal on Thursday, came off the bench in the 79th minute and made an instant impact as his quick feet earned the free-kick from which team-mate Luke James scored the opener on 82 minutes.
Moments later, Barmby marked his Football League debut with great style as he unleashed a powerful left-footed effort that beat opposition goalkeeper Nick Pope and flew into the top left corner, sending the home supporters into raptures on the terraces.
The victory helps the Pools leapfrog York into 14th place in the League Two table and ended a run of three straight defeats, leaving them eight points clear of the treacherous relegation zone.
Elsewhere, Nick Powell helped FA Cup holders Wigan Athletic move into the fifth round with a gutsy 2-1 win over Crystal Palace at the DW Stadium. The youngster was introduced in the 74th minute, just moments before James McClean’s late winner.
Ryan Tunnicliffe made his 28th appearance for Ipswich Town, playing a full match as the Tractor Boys secured a first win of 2014 with a 2-0 triumph over Reading. Mick McCarthy’s side are now up to seventh in the Championship, just a point from the play-offs.
Michael Keane was an unused substitute for Derby County, who drew 1-1 with Blackburn Rovers at Ewood Park. The Reds defender has made eight appearances for the Rams since joining Steve McClaren’s side in December.