The practice of websites streaming albums before their official release is fairly commonplace nowadays, but hats off to The Rapture for adding a touch of novelty to the idea: three weeks before their new album In The Grace Of Your Love hit shops, the Brooklyn band trained a camera on a turntable set up in their label's offices and transmitted a live webcast of the record being played from start to finish. Every few minutes, an unidentified torso interrupted the shot to hold up a card bearing the marker pen-scrawled song title, or to flip the vinyl.

With its endearingly shoddy DIY production values, the webcast served as a fitting homecoming, celebrating the band's return - following a near-decade long foray into major label limbo and recent shake-ups (original frontman Luke Jenner left the band in 2008 following the death of his mother, then returned, only for bassist and co-vocalist Matty Safer to depart for good soon after) - to the DFA fold. It's hard to imagine another high-profile indie imprint (Kompakt, for example) premiering such eagerly-awaited new material in such a way, let alone the band's former Universal paymasters, but DFA boss James Murphy's nonchalant “if it's good, it's good” ethos and rough-round-the-edges approach to recording and releasing music fits The Rapture like a glove.

They certainly sound more at home here than when last we heard from them. Recorded with a trio of du jour indie-dance studio bods – Paul Epworth, Danger Mouse and Ewan Pearson – and with Jenner being gradually edged out of the frame by Safer, 2006's Pieces Of The People We Love came across as something of an over-cooked hotchpotch, and while it included a couple of choice moments ('W.A.Y.U.H.', 'Get Myself Into It') the album as a whole felt soulless and unfocused, as if the band themselves were being used as a convenient vehicle to showcase the various producers' latest ideas.

Conversely, the task of polishing up Grace falls to one man; Phillipe Zdar of French house duo Cassius, who employs the same kind of gritty pop sheen he used on Phoenix's last album to resurrect the Rapture of old without merely aping the distinctive DFA production sound Murphy and Tim Goldsworthy introduced on Echoes.

Zdar undeniably deserves some credit, but it's the band's ability to recognise their own strengths and weaknesses that makes Grace such a success. Never ones to shy away from wearing their influences on their sleeves, Jenner, Gabriel Andruzzi and Vito Roccoforte here revisit much of the musical territory covered on previous efforts, but although the angular sounds of New York's late 70s / early 80s post-punk, new wave and mutant disco scenes are still evident – specifically in the Talking Heads funk of 'Never Gonna Die Again' - more time is dedicated to expanding on ideas that Echoes and Pieces touched upon only briefly. Opener 'Sail Away' is the kind of propulsive, fist-pumping stadium-rock anthem that wouldn't sound out of place closing an Arcade Fire show; 'Blue Bird' sees stomping Northern Soul and Beatles-y psychedelia colliding in a blur of shifting tempos, while 'Come Back To Me' plays with Pieces' mainstream dance textures, spinning what sounds like an accordion loop into a grinding – but surprisingly enjoyable - Euro-house workout. Elsewhere, the group's glam-rock fixation once again rears its immaculately-coiffed head: 'I Miss You' is a down-and-dirty, throbbing T-Rex-gone-electro boogie, while 'Roller Coaster' – with its wailing E-bowed guitar and splashing drums – is an inspired hybrid of Bowie's 'Heroes' and Roxy Music's 'Virginia Plain'.

The title track is a mid-album highlight, a spacious, opiated funk groove spiked with minimal inter-woven keyboard and guitar lines that recalls the glory days of the Happy Mondays, and although the album suffers slightly from a third-quarter slump (the resemblance between 'Children' and 'Sail Away' is just a little too strong; 'Can You Find A Way', meanwhile, is an ill-considered drum and bass-heavy foray into late-90s big beat), it recovers nicely with a closing salvo to rival popular music's greatest finales. You've probably already heard comeback single 'How Deep Is Your Love?', the house monster whose piano riffs, handclaps, saxophone freak-out and cheeky lift of SisQo's 'Thong Song' melody have made it the feel-good hit of the summer, but it's final number 'It Takes Time To Be A Man' that is the jewel in Grace's crown. During his hiatus from the band, Jenner spent some time in gospel choirs, and it's that joyous (holy) spirit that informs this soulful slow-burner, not just in the subtly spiritual lyrics or the celebratory New Orleans parade feel of the brassy climax, but in the air of blissful serenity that envelops the whole track. Suddenly the album's title takes on a new, quasi-religious meaning. After a tough few years, Jenner, Andruzzi and Roccoforte have come through with a new-found appreciation of the important things in life: family, friends, home, belief. It may not be the Rapture many were expecting this year, but this triumphant return to form is pretty glorious nonetheless.