The 7-6 victory for the Division One Central side in the second round came after a 2-2 draw in normal time in which Michael Gorniak`s brace for the top flight's Generals was equalled by Rovers` Elliot Bailey.
Chesham's league rivals Cinderford Town are struggling at the bottom of the table and suffered a 4-1 defeat at Division One South & West neighbours Bishops Cleeve, whose Logan Stoddart, Jacob Davidge, Jack Watts and Ieuan Crowe outgunned the Foresters` Ben Hands.
Division One Central`s bottom-markers Histon gave a good account of themselves before being edged out by the odd goal in five at the Carlsberg Stadium against Premier Division Biggleswade Town.
Conrad Logan gave the hosts a first-minute lead that Will Gardner cancelled out from the spot in the 24th minute, only for Andrew Iwediuno and Ihih Effiong to stretch the Waders lead to 3-1 by the 70th minute, with Jos Gwynne`s penalty accounting for the Stutes' second six minutes from time.
Biggleswade`s league rivals Basingstoke Town, St Ives Town and Stratford Town all progressed, with the latter winning the all-Premier Division derby at home against league leaders Leamington 4-0 with goals from Will Grocott with two, Michael Taylor and a Richard Gregory spot-kick.
Basingstoke saw off Division One Central side Fleet Town 4-1 at the Camrose, courtesy of Joe Gater, a Richard Whittingham penalty, Sam Deadfield and Aaron Jarvis – Ben Toye replying.
St Ives put their league struggles behind them to win 3-0 at home to Division One Central side Bedford Town, thanks to a Dubi Ogbonna brace after Josh Dawkin`s 50th minute opener.
Salisbury FC won the all-Division One South & West derby at the Ray Mac against Winchester City with goals from Tommy Wright in the 71st and 86th minutes in front of the week`s biggest League Cup gate – 348.
Not far behind was the Devon derby with 320 watching Bideford lose 4-1 at home to Barnstaple Town, whose Dave Pearse scored twice to add to Ryan Turner and Niall Heeney efforts, with Sam Stephens netting Biddy`s consolation.
The Oxfordshire derby saw Premier Division Banbury United triumph 2-0 at Division One South & West North Leigh, with Darius Browne and George Jeacock`s goals in either half.
Tuesday`s other tie saw an all-Division One Central encounter between Royston Town and Chalfont St Peter go the way of the visitors at Garden Walk, with Alan Hedley on the hour-mark and Kofi Lockhart-Adams four minutes later, outscoring Frazer John on 69 minutes.
Wednesday night's single tie saw another Division One Central outfit, Aylesbury United, oust Division One South & West hosts Kidlington 2-1 with Reece Cameron giving the Ducks a 10th minute lead that Lewis Coyle cancelled out from the spot on 32 minutes, with Taylor Collins winning it nine minutes from time.
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