Raducanu arrived in Eastbourne as the British number one, having enjoyed a run to the quarter-finals at Queen’s a fortnight ago.
But as she prepares for her fourth Wimbledon appearance – where she has twice reached the fourth round – her performance at Eastbourne looked laboured.
Some impressive serving in the opening set gave Raducanu the upper hand, but a commanding second-set performance from Joint levelled the match.
World number 38 Raducanu pulled out of the Berlin Open last week because of a back issue but, while she seemed uncomfortable at times, she did not call for the trainer at any point against Joint.
Raducanu held back tears after securing victory against Ann Li on Tuesday and said she was “mentally not really present” at points during that match.
She slumped in her chair at times on Wednesday, shaking her head in frustration – but she dialled back in to produce a thrilling end to the third set.
After breaking Raducanu in the first game of the decider, Joint saved break-back points at 3-2 and then broke for a second time as Raducanu followed a double fault with a long forehand.
But Raducanu rediscovered some momentum, twice breaking as Joint served for the match – and she even seemed to surprise herself with a remarkable break to love for 5-5.
The to-ing and fro-ing continued, both players exchanging breaks before Raducanu denied Joint for a third time as she served for the match and forced a tie-break.
But an unfortunate net cord paved the way for Joint, who took the lead and sealed her place in the quarter-finals with an ace.
Joint, who was ranked 684th in the world at the beginning of 2024 but has jumped to a career high of 51st, will face world number 69 Anna Blinkova in the last eight.
Earlier on Wednesday, reigning Wimbledon champion Barbora Krejcikova saved match points against a British player for the second day in a row to reach the quarter-finals.
Jodie Burrage held three match points on Krejcikova’s serve in the deciding set but the Czech, playing only her sixth match this year after a lengthy lay-off with a back injury, battled to a 6-4 4-6 7-6 (7-3) win.
Burrage’s fellow Briton Francesca Jones also went out in the second round, losing 6-2 6-1 to Ukraine’s world number 42 Dayana Yastremska.