Barrow beat Ipswich 2-0 in a second round replay after the initial tie ended honours even at Portman Road earlier this month.
The Bluebirds gave a commanding first-half performance and led by two goals at the break, thanks to Whites academy graduates Stevens and Gotts, who both joined Barrow from Thorp Arch in the summer.
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In his three seasons as a Leeds player, Stevens made six senior appearances for the Whites and was sent out on loan to Swindon Town and Bradford City before being sold in August.
Gotts, meanwhile, joined the Whites at under-18s level, made three first-team appearances, and was loaned out to Lincoln City and Salford City before his permanent departure this summer.
Between them, the Whites youth products have since accrued 36 appearances for Barrow, who are three points clear of the drop zone in League Two.
Both players appeared as the Bluebirds held Ipswich to a 0-0 draw in the FA Cup, a result which sealed the sacking of Tractor Boys’ boss Paul Cook, with Gotts starting and Stevens stepping off the bench in the 86th minute.
The two former Whites players were both in Mark Cooper’s starting eleven for the replay on Wednesday.
Gotts looked frustrated when, given an early chance to strike from close range, his shot flashed over the bar.
In the twenty-sixth minute, though, Gotts assisted Stevens for the opener. A cleverly-worked corner found Stevens on the edge of the box, and the winger’s first-time strike hit the top corner to give Barrow the lead.
The pair combined again to create a chance for the home side, with Stevens finding the front-post run of Gotts, who fired over again.
The midfielder got his moment, though, when Patrick Brough nodded Stevens’ cross back across the box for Gotts to tuck home from six yards out.
Ipswich regained some control over the game in the second half but weren’t able to recover the tie, which ended in a 2-0 victory for Barrow.
The Bluebirds now face a third round tie against Championship side Barnsley at Oakwell in January.
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