Goals from Scott Brown and Garry O'Connor secured their passage and gave them hope this could be their year to go all the way after a 103-year separation from the trophy.
Hibs threatened first and came close after eight minutes. Derek Riordan released O'Connor and his shot across the face of the goal looked to have been touched past the post by Craig Hinchcliffe but referee Willie Young gave a goal-kick.
Five minutes later, Hinchcliffe did get a touch as he slapped away another shot from O'Connor and Hugh Murray scrambled the ball for a corner at the far post before Riordan or Steven Fletcher could turn home the loose ball.
But St Mirren defended stubbornly and restricted Hibs to few openings in the first half. Gary Caldwell even presented one to the first division side when he did not get enough on a pass-back, but Alan Russell could not take advantage.
But it took a terrific save from Hinchcliffe after 32 minutes to keep St Mirren level. Scott Brown laid the ball back to O'Connor, whose 25-yard shot was bound for the top corner before Hinchcliffe tipped the ball over.
Saints had a chance two minutes from the break when Hibs were absent-minded with their marking, but Stewart Kean failed to make contact with his head from six yards with the goal at his mercy.
Hibs punished them on the stroke of half-time. O'Connor slipped the ball through to Brown, who drove a firm right-foot shot past Hinchcliffe into the net.
St Mirren opened out more in the second half and David Murphy had to hook a Kirk Broadfoot header off the line following a Murray corner.
But there was no way back in the 74th minute when Hibs scored their second goal. Antonio Murray caught the Saints' defence square with a long through ball, and O'Connor galloped round Hinchcliffe and slipped the ball into the net.
Murray almost scored a third moments later, but his 25-yard shot cracked against the post.