The woman, named locally as Leanne Bowman, died along with a man, thought to be James Coleman, in the incident in Beeston on Saturday.
Another man was seriously injured.
The three people – all thought to be from the local area – were in a Ford Focus that was involved in a head-on collision with a lorry on Middleton Grove at 5.30am.
It is thought the lorry may have been parked at the side of the road when the crash happened. Its driver was not injured.
Police closed the road for several hours after the incident while investigations took place and have appealed for anyone with information about what happened to come forward.
Floral tributes have been left at the scene. One message read: “RIP Leanne. Will be missed by many.”
Another, addressed to “Leanne and James”, said: “Sleep tight, will be missed. Thinking of you.”
One bunch of flowers carried a picture of Miss Bowman with two children.
The accident happened close to a slight bend in the road, which is in an industrial area not far from the John Charles Centre for Sport.
Calls have already been made on social media for traffic calming measures on the road, where there is a 30mph speed limit.
But Angela Gabriel, councillor for Beeston and Holbeck, said the spot did not have a track record of incidents.
She said: “We’ve never had any trouble there as far as I know. Kids walk up and down that road to school and there’s never been an accident.”
Friends and relatives spoke of their loss on social media sites. One wrote that Miss Bowman was a “beautiful person”.
Anyone with information should call the West Yorkshire Police major collision enquiry team via 101.