The visitors took the lead in first-half injury time through a Shaun Harrad penalty but a leveller from Sam Clucas in the 74th minute gave the home side hope and dragged the game into the extra half-hour.
But Yusef's strike clinched the win for the Robins, whose reward is to welcome the Barclays Premier League side to Whaddon Road in the first week of January.
League Two Southend pulled off a minor upset to beat League One strugglers Bury 3-2 on penalties at Roots Hall after a 1-1 draw after extra-time. Zac Thompson's opener was quickly cancelled out by Gavin Tomlin for the Shrimpers.
David Worrall, Troy Hewitt and Mark Hughes all missed spot-kicks for Bury, meaning Southend go through to a third round home tie against Brentford, pending an appeal by Bradford City over their expulsion.