Manson’s cross was headed back across goal by McArthur and Strickland headed home from close range.
Mackenzie was booked for a foul on Seely as the Rose chased back following some good play in the Beath box and a couple of minutes later McArthur nearly doubled the lead.
The Rose continued to dominate the first half and created a number of opportunities.
Just before the half hour mark keeper Hall had to stretch to deny Smith and Strickland was unlucky that his shot on the turn went just over the bar.
A few minutes later, Ruari MacLennan committed a bad foul on Bathgate for which he was booked.
It wasn’t until the 38th minute that Hay had his first save to make.
Bathgate was through on goal but the keeper saved with his legs. Just a minute later another rash challenge by MacLennan on Gemmell saw the Rose man receive a second yellow card and he was sent off.
Shortly before half-time, a rare mistake by Mackenzie allowed Smart to play in Bathgate only for keeper Hay to bring him down near the by-line.
The referee had no hesitation in awarding a penalty which Bathgate himself converted.
The Rose started the second half with an early goal. Nelson found Walker and his low shot from the edge of the box beat Hall.
Ten-man Rose battled hard but Beath began to dominate and, in the 57th minute, levelled the scoring when Adamson’s cross was knocked back by Smart and Smith scored.
Shirra replaced Strickland but Beath went ahead in 69 minutes when Hay fumbled McCulloch’s long range effort and Dair followed up to score.
Rose threw on Herd and Coyne to replace McArthur and Benton, but Beath looked comfortable.
However, in added time, Tyrell’s long pass was headed down by Coyne to Manson who worked a neat little one-two with Herd before sending a fine shot low past Hall to take the tie to penalty kicks.
Coyne, Shirra, Manson and Tyrell all scored for the Rose and a miss by Smart and a great save by Hay from McCulloch sent them through to the next round and keep their season alive.
Rose man of the match: Smith
Rose: Hay, Benton (Coyne 71), Tyrell, Mackenzie, Walker, Ruari MacLennan, Manson, Nelson, Smith, Strickland (Shirra 59), McArthur (Herd 71). Subs (unused): Brown, Fleming, Bradley, Allison