Elain Cooper from the Liberal Democrats won in Parkside, while Labour s Chris Slough returned to the town council after securing the vote in Tithe Farm.
The Conservatives did not contest either seat, nor were there any representations from independent candidates.
Houghton Regis Liberal Democrats stated: "Congratulations to our candidate Elaine Cooper who as been elected for the Lib Dems on Parkside. However, we lost out on the seat on Tithe Farm by 33 votes - we would like to say a big thank you to Brendan Gilmartin who was our candidate."
Dunstable and Houghton Regis Labour Party wrote online: "What a few weeks it has been! Our Labour members and candidates for the Tithe Farm and Parkside by-elections have thoroughly enjoyed the many conversations we've had on the doorsteps across the town, and discussing the priorities residents have for the future.
"Thank you to everyone who has voted for Chris and Rigerta in this election, and to all the Labour members who have given up their time to support them in this campaign."
The full results were as follows:
Elain Cooper (Lib Dem) - 409
Rigerta Ahmetaj (Labour) - 233
Brendan Gilmartin (Lib Dem) - 292
Chris Slough (Labour) - 322