Barnet saw off League One Colchester in the first round of the Johnstone's Paint Trophy, while Bournemouth were impressive victors.
Cheltenham and Southend are also through, while Exeter and Brentford required penalties to book their safe passage.
Barnet sent third-tier Colchester packing after leaving the Weston Homes Community Stadium with a 3-1 win, with Izale McLeod among the goals for the Bees before being sent-off.
A second-half blitz from Bournemouth saw them to a 4-1 victory over Hereford, with Jayden Stockley stepping off the bench to bag a brace.
Cheltenham prevailed in their meeting with League Two rivals Torquay, with a 2-1 win enough to book their place in round two.
Liam Dickinson had an eventful night with Southend, bagging the only goal of the game in their tie with Crawley and seeing red for violent conduct.
Exeter were held 1-1 by Devon rivals Plymouth, but the Grecians held their nerve in a shootout to secure a 3-0 success.
MK Dons and Brentford played out a six-goal thriller at Stadium:mk, with the game producing own goals, dismissals and penalty kicks, but it was to be the Bees who went through 4-3 after a shootout.