The Daniels welcomed back Cleveland Taylor, Tom Siddons and James Hicks after they all missed the win over Belper Town in the last round.
Stamford enforced inactivity was clear to see as home side came racing out of the blocks and forced a couple of early corners.
Halesowen opened the scoring on four minutes when a cross from the right was met by Jamie Molyneux, but his header was against the post, but Robbie Bunn was on hand to tap into an open goal. The home nearly doubled their lead when Montel Gibson put his effort wide with the Daniels goal at his mercy.
Gradually Stamford started to get their passing game together and just after the half hour mark, the Daniels had a great opportunity to level the score. Good build up saw Cosmos Matwasa feed the ball to Tom Siddons and his shot was well saved by Brendon Bunn in the home goal.
Halesowen was still looking dangerous and Gibson crossed the ball from the right but Molyneux was not able to connect with the ball as it flashed across the 6-yard box.
The Daniels were level three minutes before half time when Ollie Brown-Hill picked the ball up in midfield and ran at the home back line. He unleashed a shot from 20 yards and the ball took a big deflection which left Bunn stranded as the ball sailed into the net.
As the half closed, the Daniels almost took the lead as Matwasa fed the ball to Brown-Hill, but his shot was over the bar.
At the start of the second half, neither side carved out many clear-cut chances and the first effort of note came just after the hour mark when James Blunden headed the ball goalwards but Bunn was able to save the effort. Stamford did take the lead on 71 minutes when the Daniels were awarded a free-kick on the right of the penalty area and Harry Vince whipped in the free-kick which was met by Tom Siddons to head home his ninth goal of the season.
Halesowen pressed Stamford looking for an equaliser and had a couple of efforts none of which tested Dan Haystead in the Daniels goal.
Their pressure finally told as on 89 minutes. A long ball downfield by the home keeper was controlled by Montel Gibson and his shot came of the post and into the goal to force a replay and the chance to meet Grantham Town in the next round.