The conference outfit rocked the Merseysiders with two goals in a seven-minute spell and it was game-on again.
But Tranmere settled and finally made sure of progress with their fourth goal after 83 minutes.
Steve Davies ran the show for Tranmere, but Gareth Taylor and Chris Greenacre provided a terrific threat and helped themselves to two goals each.
Woking created little in the opening half, although Craig McAllister did hit the top netting early on.
Tranmere went ahead in the 19th minute. Taylor headed home off a post from a Davies corner.
Taylor was unlucky to see a goalbound shot superbly turned over the bar by Woking keeper Shwan Jalal in the 28th minute but it was 2-0 after 37 minutes with a Davies cross being neatly turned in at the near post by Greenacre.
Tranmere struck again two minutes after the re-start with Taylor again heading in from close-range from a well placed cross by Greenacre.
But Woking suddenly came alive, although it was out of the blue when they pulled a goal back in the 63rd minute.
McAllister and home keeper Gavin Ward challenged for a Simon Jackson cross and as the ball ran free it appeared to go in off Tranmere skipper Shane Sherriff.
Woking struck again in the 69th minute. McAllister found the target with an excellent right-foot shot from the edge of the box when set up by Guiseppe Sole.
The Merseysiders showed some signs of panic and Gary MacDonald fired over from 30 yards for the visitors.
But it was all over in the 83rd minute when Greenacre netted from close-range after Taylor headed down a Davies corner.
Karl Murray and McAllister worked hard for Woking but they were caught out at the back on too many occasions.