The bottom-of-the-table clash was, on paper, a 'must-win' game for Jesse Marsch's side, whose poor recent form left them just two points clear of the drop zone.
Leeds dominated the visitors in the first half and were unfortunate to take just a one-goal lead, courtesy of Rodrigo's 14th-minute strike, into the interval.
The Whites squandered chances aplenty after the break and rued their misses when Kenny McLean equalised for Norwich City in injury time.
Marsch acted decisively in pursuit of a win, bringing on young United striker Joe Gelhardt in the hopes the teenager could bag a winner.
The 19-year-old delivered in scintillating fashion, tapping in from a Raphinha cut-back to the delight of the Elland Road faithful.
United now sit four points clear of the drop zone and, crucially, have kept relegation rivals Norwich at bay.
The YEP's Tony Johnson was on hand to capture the joy and the despair in the Elland Road stands.
1. Leeds United v Norwich City
A young fan with a plea for the Whites players before kick off. Photo: Tony Johnson
4. Leeds United v Norwich City
Rodrigo celebrates in front of the Elland Road crowd. Photo: Tony Johnson
6. Leeds United v Norwich City
Leeds fans show their support for Ukraine. Photo: Tony Johnson