World Series champion Couch scored 339.70 points in the semi-final to qualify for Thursday’s showpiece event in seventh place.
Any divers who reached the final automatically claimed a quota place for their county at the Rio Olympics.
Couch dived consistently all afternoon, scoring between 64.00 points and 73.60 for her six dives.
She said: “I’m chuffed to make the final because it’s been a very tough day, starting at 7am and finishing at 4.30pm.
“I think it showed on everybody because a lot of divers didn’t dive their best today but I think it will be different tomorrow.
“Getting that Olympic quota place is great and take a little bit of weight off my shoulders.”
However, there was disappointment for her city team-mate and European champion Sarah Barrow, who missed out on the reaching the final.
Barrow, who has been struggling with stress fractures in her shins, dropped two of her dives in a high quality semi-final to finish 19th on 283.10 points. She had finished fourth at the last World Championships in Barcelona.
Couch and Barrow had gone through the preliminary round just a couple of hours before the semis. The preliminary round involved 37 competitors making 185 dives.
Barrow said: “I’ll take a couple of months now to let my shins heal and, hopefully, next year I can come back injury-free.
“The first dive was better than this morning but it’s been such a tiring day and I really felt like I didn’t have much energy going into that.
“I’ve been injured this year, so I was missing that endurance you need to compete at this level.”