The South Africa striker stepped off the bench in the 73rd minute with his side trailing 2-1 to their promotion rivals and two minutes later sent a right-footed volley from Luciano Becchio's flicked header arrowing into the bottom corner.
Becchio had headed Leeds deservedly in front in the 16th minute, but Henri Lansbury fired Norwich level in first-half stoppage time.
Wes Hoolahan clipped home the Canaries' second to the delight of their travelling hordes in the 69th minute before Somma rescued a deserved point for Simon Grayson's side in a super advert for second-tier football.
Becchio and Leeds skipper Jonny Howson both struck the woodwork in the first half and Norwich's leading goalscorer Grant Holt hit the post in the second as two accomplished teams went head to head in front of a captivated audience of 31,601.
Leeds sent out the same line-up that started last week at Bristol City, while defender Zac Whitbread and striker Aaron Wilbraham returned for Norwich.
Howson had the game's first chance, bursting forward to shoot inches wide in the fourth minute, while Becchio headed Robert Snodgrass's free-kick onto Norwich goalkeeper John Ruddy's left-hand post soon after as the home side started with menace.
Leeds were rewarded for their early energy and accurate passing with the opening goal in the 16th minute.
Max Gradel's cross from the left was flicked on by Snodgrass and Becchio brushed aside Norwich left-back Adam Drury at the far post to head home his 15th goal of the season.
Norwich began to find their feet 10 minutes before the break and following some neat possession David Fox forced a flying save from Kasper Schmeichel with a 25-yard shot that was otherwise destined for the top corner.
But only the woodwork denied Leeds a second goal in the 38th minute.
Full-back Eric Lichaj, on loan from Aston Villa, drilled in a low cross and when Ruddy blocked Howson's first effort, the Leeds skipper fired the rebound against the post.
But Leeds were dealt a blow in first-half stoppage time when Lansbury lashed home a low shot inside the near post following Grant Holt's knockdown from Andrew Crofts' cross.
The encounter lost none of its rhythm after the break. Leeds left-back George McCartney's shot was smothered by Ruddy and Hoolahan's similar effort at the other end was fumbled away for a corner by Schmeichel.
Leeds produced the best move of the game in the 55th minute, with McCartney, Gradel and Snodgrass combining to send Howson clear, but the midfielder's low drive was deflected agonisingly wide.
Gradel dragged a volley off target three minutes later.
But Norwich served warning of their intentions when Holt flicked the ball onto the post and within two minutes the Canaries stole into the lead.
Crofts played in Hoolahan and the Norwich midfielder's low right-footed shot beat Schmeichel and Lichaj, who could only deflect the ball into the net.
Leeds manager Simon Grayson sent on striker Somma for midfielder Neil Kilkenny in the 74th minute and within another 60 seconds he volleyed the ball beyond Ruddy for a fine equaliser with his very first touch.
Late substitute Billy Paynter almost snatched all the points for Leeds in the closing seconds, but was denied by Ruddy at full stretch as the drama lasted right up until the final whistle.