Stepney, who was given a wild card entry to the Co-op Funeralcare International Open in Blackpool, beat six-time world indoor champ Andy Thomson in round one on Saturday.
His reward is a second round ,atch against another former world champ, fellow Scot David Gourlay who beat Stepney in the final of the Scottish international open last year.
Stepney, from Burghead, kept his nerve in a tiebreak set to oust Englishman Thomson, who has won both indoor and outdoor world titles during an illustrious career in bowls.
The Moray man was always in charge of the first set, leading 6-3 after six ends and even three shots by Thomson in the eighth end wasn't enough to stop Stepney claiming an 8-6 success.
Keen to finish things off in the next, Stepney led 6-5 going into the final end but the number 10 seed pulled off a double to snatch the set and tie the match up.
Stepney won the first end of the tiebreak, Thomson edged the next and it was left to the Elgin stadium bowler to conjure up one last winning bowl in the decider to claim a close victory.
Gourlay beat Hong Kong's Chris Chau in two sets to book his meeting with Stepney on Tuesday.
Stepney had to get a wildcard to reach the Scottish international open in Perth late last year before embarking on a superb run all the way to the final.
He beat fellow Scot Stuart Anderson, English pair Perry Martin and Mervyn King, then multiple world champ Paul Foster in the semis before succumbing to the superior bowls of Scotland coach Gourlay in the final.