The league leaders took just four minutes to break the deadlock, with Dutch striker Zeefuik continuing his impressive form in front of goal by latching onto a long ball and curling a low shot into the corner.
Basement boys Livingston quickly recovered from their shaky start and began to match Hearts across the pitch, but were unable to penetrate their defence during the first period.
That changed shortly after the break when Craig Sives stunned the Jambos with a deserved equaliser, rifling home at the back post after collecting a long throw-in inside the box.
Zeefuik almost put Hearts back in front with his second of the afternoon moments later, turning on the edge of the box and firing narrowly over the crossbar.
Livingston looked the more likely to take maximum points in the latter stages, but two goals in as many minutes left them shellshocked, the first coming in the 82nd minute from substitute Kenny Anderson, who marked his Jambos debut with a headed goal.
Hearts edged their noses further in front straight from the restart as Billy King lined up Walker for a shot inside the box and the midfield fired home, but there was more late drama to come.
Kyle Jacobs stepped up and fired the resulting penalty beyond Alexander, but it was too late to prove anything beyond consolation for spirited Livingston.