Boro keeper Chris Day denied the Dons victory in the shoot-out when he saved Peter Leven's penalty, before Doumbe blasted his effort over the bar. Boro substitute Darius Charles had earlier blasted a stoppage-time equaliser to cancel out Lewis Guy's 49th-minute opener for the Dons.
Conference South side Woking came up just short at home to Brighton, losing 3-0 on penalties after a 2-2 draw.
They looked on course for an upset when Ola Sagbanmu scored in the 103rd minute but Elliott Bennett levelled for the visitors, who then had their assistant manager Mauricio Taricco sent off seconds later.
Huddersfield stunned Cambridge with a pair of stoppage-time goals to beat the Blue Square Premier team 2-1 in a dramatic climax to their replay.
Lee Clark's League One outfit looked like slumping to a dismal 1-0 defeat at home, with Rory McAuley's 53rd-minute goal almost enough to cause an upset. However, Lee Peltier levelled up for the Terriers in the first additional minute and Gary Roberts fired in the winner three minutes later.
Dartford's failure to finish off Port Vale in the first game between the teams, when they conceded a late equaliser, cost them dearly as the Conference South side were thrashed 4-0 at Vale Park.
Marc Richards scored twice, the first a penalty, and there were also goals for Sean Rigg and Justin Richards for Vale, who will meet Accrington in the second round.
James Brown headed Hartlepool into the second round after he converted Evan Horwood's cross in the 70th minute at Rivacre Park to dump Vauxhall Motors out and earn a home tie against Yeovil.
Huddersfield's reward for their late comeback will be a home tie against Macclesfield after the Silkmen knocked out Southend 5-3 on penalties following a 2-2 draw.
Wade Small's eighth-minute strike secured a 1-0 win for Aldershot against Brentford, and they will meet Dover next.
Peterborough pummelled Stockport 4-1 with goals from Kelvin Langmead, Craig Mackail-Smith, Lee Tomlin and Aaron Mclean - Greg Tansey replying. Peterborough will travel to Bury in the second round.
Fleetwood were beaten at the second attempt by Walsall, who had goalkeeper Jimmy Walker to thank for a draw in the first match between the teams. Walsall were improved and won 2-0 with both goals from Reuben Reid. A trip to Torquay awaits them in the next round.
Leyton Orient were pushed hard by Dagenham and Redbridge in a keenly contested derby at Brisbane Road, but eventually prevailed 3-2.
Scott McGleish and Alex Revell put the home side 2-0 up early on, but two goals inside a minute midway through the second half - a penalty from Danny Green and long-range strike from Solomon Taiwo - hauled Dagenham level. However, McGleish fired in his second goal of the evening for Orient in the 76th minute and they can look forward to a televised second-round clash with Droylsden on November 29.