Middlesbrough also went down and Newcastle, needing to better Hull City's result against Manchester United [ Images ], produced a lacklustre second-half performance against Villa despite the fact that an equaliser would have saved them.
Hull lost 1-0 at home to champions United, for whom Darron Gibson [ Images ] scored a stunning goal, but stayed up with a meagre 35 points after winning just one of their last 22 league games.
Hull manager Phil Brown took the microphone after the final whistle and sang to the delirious Hull fans who can look forward to a second season in the top flight.
Middlesbrough's slim hopes of avoiding the drop were extinguished by a 2-1 defeat at West Ham United and Sunderland's 3-2 home loss to Chelsea [ Images ] did not prove costly.
Hull finished one clear of the drop zone with 35 points from 38 games, above Newcastle on 34 and Middlesbrough and West Bromwhich Albion on 32.
Liverpool set a new Premier League points record for a team finishing runners-up, capping their impressive challenge to Manchester United with a 3-1 home win over Tottenham Hotspur [ Images ].
They finished with 86 points, four behind United who clinched the title last week and sent out a virtual second-string side against Hull as they prepare for Wednesday's Champions League [ Images ] final against Barcelona [ Images ] in Rome.
Fulham [ Images ] claimed the final European qualifying spot, finishing seventh despite losing 2-0 at home to Everton who came fifth.
Newcastle's 16-year stint in the top flight ended with barely a whimper at Villa Park.
The goal that sent them down summed up events at St James' Park this season during which four different managers have been in charge.
Gareth Barry's [ Images ] shot was going harmlessly wide until it cannoned off Duff and flew into the bottom corner of Steve Harper's net.
Obafemi Martins came closest to equalising for Newcastle just before halftime but they offered little after the break and were lucky not to lose by a bigger margin.