The Cherries thrashed the Toffees in the third round of the cup.
FrankLampard made 11 changes and his side lost to Bournemouth.
Junior Stanislas finished following a defensive error after Gary O'Neil's side led via a deflected shot.
Bournemouth secured their passage after Emiliano Marcondes and Jaidon Anthony scored.
Before the World Cup comes up this weekend, O'Neil and Lampard made wholesale changes to their teams.
Mark Travers and Chris Mepham were the only two players to keep their places for the home team.
Lampard completely changed his starting XI from Saturday's defeat to give a first start to James Garner.
The new-look Cherries took the lead after seven minutes when Lowe's effort hit Nathan Patterson and looped into the net.
In the first 16 minutes, Tom Davies blasted a one-on-one over, while Anthony Gordon's headed over the bar was the best chance of the half.
Gordon should have been sent off for a two-footed lunge on Jordan Zemura shortly before half-time, but instead got away with his seventh booking of the season.
The chance of a first major trophy in 19 years was upset by the decision to make so many changes by Lampard.
Since taking over as interim Bournemouth boss, O'Neil has overseen four defeats in a row.
However, a cup run will do his chances of a permanent appointment no harm, although had they taken their chances it would have been very different.
Stanislas scored a goal for Bournemouth on the 47th minute. Ryan Christie stole it as Mason Holgate slipped and fell.
He squared to Lowe, whose shot was blocked, but it rebounded to Stanislas, who tucked away with a covering defender.
Alex Iwobi and Gray were thrown on to try to rescue the match, and the latter made an impact on 67 minutes by curling the ball past Travers.
Bournemouth have given away two-goal leads in their past two games, but on this occasion they took their chances to win.
O'Neil's chances of keeping the manager's job on a full-time basis have increased after Marcondes and Anthony found the back of the Cherries net.
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