for instance:

'Take Me to the River' from the Talking Heads
'Movin' On Up' - Primal Scream

what else?

'Shine a Light' - Rolling Stones

My Sweet Lord - George Harrison
Spirit in the Sky - Norman Greenbaum

Not sure I understand the topic, are we looking for gospel covers (Take Me to River) or originals in the gospel vein?

If it's the latter here are a couple:

All These Things I've Done- The Killers
Like a Prayer- Madonna
Just a Man- Faith No More

no sorry, songs that are a mixture of the two, so yes, The Killers and Madonna songs are what I'm asking for,

or even the simple use of a gospel choir

example:
Linda Ronstadt's songs: 'So Right, So Wrong' and 'Cry Like a Rainstorm' (okay, now I want to relisten to that whole entire album - one of my faves)

The Beatles - Let It Be (no gospel choir per se, but it definitely feels like a gospel tune)
Elton John - Border Song
George Harrison - Awaiting On You All
Blur - Tender
Talking Heads - Road to Nowhere
Wilco & Billy Bragg - Airline to Heaven (the version from Mermaid Ave., Volume 2)

Not specific songs, but Robert Randolph, B.R.M.C.'s Howl, and a healthy chunk of Spiritualized's output have what you're after.

Love is the Answer - Todd Rundgren or England Dan & John Ford Coley

Springsteen's My City of Ruins is structured like a gospel song, the chord progression is almost identical to "People Get Ready"

A couple more:

good call on Spirtualized, I'd recommend "Come Together"

Joy to the World- Three Dog Night
I Still Haven't Found What I'm Looking For- U2, kind of an interesting one, a rock song that became a staple of gospel choirs after its release.