Adam Idah found the net on his Norwich return following a six-month injury lay-off, but the Canaries ultimately exited the Carabao Cup on penalties.
The Republic of Ireland striker thought he had marked his return with a late winner off the bench, only for Brooklyn Genesini to pull Bournemouth level in stoppage time and secure a 2-2 draw to take the tie to penalties.
Earlier, Emiliano Marcondes had cancelled out Jordan Hugill’s opener for the hosts as Angus Gunn shone in goal at Carrow Road.
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Idah had been sidelined since February after suffering a serious knee injury, but stepped up his recovery in recent weeks.
Hugill, whose Norwich future remains in doubt amid reports of a return to Cardiff, was on hand to turn home after Neto – making his Bournemouth debut having signed following his release from Barcelona – could only push a low Gabriel Sara shot into his path.
Christian Saydee, drafted into the Bournemouth side after Jamal Lowe complained of illness during the warm-up, struck the crossbar from close-range as the visitors chased a leveller.
The equaliser would come just before the break, Marcondes left with a simple finish after the ball fell to his feet following a Gunn parry.
Scott Parker’s side were now the more dangerous with Saydee forcing a smart stop from Gunn early in the second half.
The former England Under-21 international was being kept busy between the posts, Ryan Christie the next man denied as his lob was kept out.
With Norwich’s attacking intent petering out, Dean Smith responded by introducing Temmu Pukki and Idah with 20 minutes remaining.
Gunn was keeping Norwich alive in the tie – saving his best for a point-blank block from Anthony as Norwich countered at pace to retake the lead.
Pukki showed his nous as he broke into the box and put a low cross in which Idah finished for just his second goal in the past 15 months, only for fellow substitute Genesini to strike late on.
With the first three penalties converted it was Cantwell – who made 11 appearances for Bournemouth as they were promoted to the Premier League last season – who cracked the crossbar with his attempt.
It proved to be the only miss of the shoot-out as Bournemouth scored all five, Christie holding his nerve to send Parker’s side into the next round with the final effort.
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