But they had to withstand plenty of pressure from Woking, particularly when the visitors pressed in the second half.
Stafford, looking to build on Tuesday's victory at Gravesend, had the game's first attempt on goal. Inside the first minute, Robin Gibson tried his luck from out on the left but his shot was comfortably collected by Woking keeper Shwan Jalal.
A mistake by Craig Lovatt, mis-hitting an attempted back-pass, gifted a first corner to the visitors. Delivered by Guiseppe Sole, the ball wasn't cleared and Danny Alcock held a header from Craig McAllister.
However, Stafford with an unchanged side, continued to make a bright start. Ged Murphy thumped a shot at Jalal before Rangers took the lead in the eighth minute. Nathan Talbott robbed Goma Lambu and delivered a defence-splitting pass. Madjo got on the end of it and scored with a clever lob over the advancing Jalal.
Madjo continued to cause problems and he created another opportunity for Gibson with a deep cross. The winger ended up firing tamely at the Woking keeper from a narrow angle.
Woking found scoring chances limited and skipper Neil Smith went for goal from distance but Alcock was well-positioned to gather up the resulting low 30-yard drive.
There was further danger for Stafford midway through the half. McAllister headed down a deep cross and Lovatt hurried cleared the ball from in front of goal at the expense of a corner.
Rangers found chances restricted themselves but a knock-down on 28 minutes by Madjo fell to Kevin Street. However, the midfielder fired wide of the near post.
As the interval approached, play was largely confined to the middle third of the field with defences on top.
Sole sent two efforts over the Rangers bar before Woking thought they had equalised in he 43rd minute. Ollie Berquez headed home only to be thwarted by the raised flag of an assistant.
Woking made a change at the interval with Saheed Sankoh replacing fellow attacker Lambu. He lifted the visitors attack and helped his side dominate the second half.
Both sides were awarded free-kicks in dangerous positions soon after the restart. Wayne Daniel headed wide from Street while Woking's free-kick caused plenty of problems for the Stafford defence. The ball bobbed around inside the area before Tom Hutchinson headed over.
The game certainly opened up. Grayson forced Jalal into a near-post save and sent a couple other shots wide.
Karim El-Salahi was booked for a foul on Neil Grayson just outside the area but Craig McAughtrie sent the resulting free-kick over the bar.
Stafford, soaking up plenty of pressure, had the ball in the Woking net in the 71st minute. Grayson slotted home at close range but Talbott fouled Jalal in the build-up.
The closing stages saw Woking throw everything they could forward though they found the Rangers defence difficult to penetrate.
Alcock was called into action, holding a low shot drilled towards goal by the lively Sankoh and a diving header from Berquez who got on the end of Daniel Bunce's cross. McAllister also sent a low shot flashing past a post.
Woking kept on pressing with Sankoh firing wide at the near post. The Stafford keeper kept his best save for injury time. He tipped over a dipping shot from Bunce to secure three valuable points for his side.