Amy Appleton, 32, was killed with 76-year-old Sandy Seagrave on Hazel Way, Crawley Down, West Sussex, on Sunday.
It is believed Ms Seagrave, who lived a short walk from the scene, tried to step in as Ms Appleton was attacked.
Sussex Police said a 37-year-old man, found seriously injured at the scene, remains on life support in a critical condition. Police said the suspect was known to one of the women.
Ms Appleton, a teacher at nearby Copthorne Church of England Junior School, was described by her family as a "beautiful, caring daughter, sister and friend".
A tribute added: "Amy had an amazing personality. She was such a strong, positive person who always smiled.
"She was a rock for her family, a rock for her friends and most of all a rock for herself. Amy always thought of others before herself."
The tribute added: "Amy led the life she was destined to fill, following her passions.
"Her school will be missing an incredible, dedicated teacher, she gave 110% to her pupils.
"Her light will always shine in our lives but a hole has been left with broken hearts.
"The whole family would like to send heartfelt thanks for all kind messages and thoughtful tributes. Keep shining our girl, you will forever be in our hearts."
It comes after Ms Seagrave's family described the older woman as "one of a kind, an eccentric character who was stubbornly independent, feisty, brave and not afraid of anything".
Sussex Police have not yet released details of how the two women died, but said it was not a knife attack and that one of the victims was known to the suspect.
Anyone with information is asked to contact police.