The victory in the first of the reverse singles gave India a winning 3-1 lead before the last match of the tie in which Izak van der Merwe faced India's 17-year-old prodigy, Yuki Bhambri, in what was effectively a dead rubber.
What was shaping into the most "memorable" victory of 29-year-old De Voest's career turned instead into heartbreak as he ran out of steam towards the end of the tense, absorbing proceedings and fell foul to the super-fit Devvarman, who finished off by playing his best tennis of the match in the last two sets.
Yet when De Voest led 6-3, 7-6 and 5-4 in the third-set tiebreaker it seemed the prized place in the World Group was destined to be decided in the last match - with South African captain John-Laffnie de Jager having brought in Wesley Moodie to replace Van der Merwe in the decider had the penultimate match gone that way.
De Voest also appeared to have victory in his grasp when he broke service immediately at the start of the third set, with Devvarman admitting afterwards that he was "frustrated" at that stage and was at his wits end as to how to turn the tide.
However, the Indian No 1 gained fresh momentum and inspiration when De Voest momentarily appeared to lose concentration and allowed Devvarman to break back to 2-2 in the third set.
And ultimately, neither Moodie nor India's Rohan Bopanna - their teams' first choices for the final encounter - played later in what was largely an inconsequential final match-up.
De Voest, however, emerged with unreserved credit for his overall performance, with nothing emphasising his grit and resolution more than the fact that he saved 20 break points through a cut-and-thrust encounter in which both players performed at an unwavering high level.
De Voest struggled to hold his opening service of the game, but after levelling the score at 1-1 struck a devastating purple patch, broke service to lead 3-2 and stormed to a first-set victory after winning his last service following a 16-point game.
The see-sawing struggle continued in the second set, with Devvarman gaining the ascendancy when he broke service to lead 6-5 - only to squander a set point with a badly mistimed smash and trail by two sets as De Voest took control of the resultant tiebreaker.
The match underwent a fateful change in direction when De Voest allowed Devvarman to break back at the start of the third set, with the Indian No 1 holding his nerve when poised at two points away from a straight-set defeat.
Devvarman dominated the fourth set and raced into a 5-1 lead by winning five successive games - and although De Voest held his opening serve in the fifth set after a 14-point game and battled grimly until the end, the writing at this point was already on the wall.
And while De Voest's bold tactics - storming the net at every opportunity against a dominant baseliner - came within a whisker of succeeding, Devvarman finally came up with the answers.
Sunday:
Somdev Devvarman (India) beat Rik De Voest (South Africa) 3-6, 6-7 (3/7), 7-6 (7/5), 6-2, 6-4
Yuki Bhambri (IND) bt Izak van der Merwe (RSA) 3-6, 6-3, 6-4
Saturday:
Doubles
Wesley Moodie/Jeff Coetzee (RSA) bt Mahesh Bhupathi/Rohan Bopanna (IND) 6-3, 3-6, 4-0 retired (Bhupathi injured groin)
Friday:
Somdev Devvarman (IND) bt Izak van der Merwe (RSA) 7-6 (7/5), 6-3, 6-4
Rohan Bopanna (IND) bt Rik De Voest (RSA) 2-6, 6-4, 6-2, 6-4