Livingston added to Partick's misery at the foot of the Premierleague thanks to first-half goals from Derek Lilley and Lee Makel.
The home side should have won by a bigger margin but some indifferent finishing and some fine goalkeeping meant they had to settle for a modest return.
Livingston made a bright start and Jon Paul McGovern tested Kenny Arthur early on with a right-foot volley. But it was Partick who had the first clear-cut chance when John Paul McBride put Jamie Mitchell through but he pulled his shot across the face of the goal.
Livingston responded and should have taken the lead in the 18th minute. The excellent David Fernandez wriggled past three defenders and cut the ball back for Lilley, who sidefooted past the post from just six yards.
Makel was then through on Arthur after a through ball from Fernandez but he failed to make contact and the goalkeeper managed to smother the ball.
The home side took the lead from the penalty spot after 25 minutes when David Rowson fouled Burton O'Brien in the area and Lilley struck home the spot-kick.
Marvin Andrews and Stuart Lovell both forced saves from Arthur before Livingston scored their second a minute from the break.
Makel robbed Derek Whyte and sent Fernandez clear and he returned the pass for the midfielder to slide home the second goal.
Lilley had another chance at the start of the second half but his header was too close to Arthur.
The Partick goalkeeper made a superb save to block a shot from Lovell after 63 minutes to divert the ball for a corner.
Arthur then made a fine double save to keep out efforts from Lovell and Fernandez and, before Partick could clear, Lovell sent a header against the post.
Fernandez was stretchered off after 77 minutes, which could cause Livingston some concerns.