Goalkeepers Chris Day and Carl Ikeme were kept busy but both had fine games to ensure a stalemate.
Wolves came close when Day beat away Nouha Dicko’s shot from a narrow angle and Leon Clarke could only head the rebound wide.
The visitors almost went behind in calamitous fashion as Kevin McDonald sliced Jimmy Smith’s corner but Ikeme bailed him out with a flying save.
Stevenage began to rally in the second half as Francois Zoko’s long pass picked out Smith with Ikeme doing well to tip his effort over.
It was then Day’s turn to be a hero in goal as he stayed big to make a great save to deny Clarke, who had been put through by Michael Jacobs.
Boro are now one point off safety with Wolves now 11 points clear of third-placed Leyton Orient with six games left.