The Swede started the day four shots off the lead and remained there at the turn before he made five birdies in a row to surge to the top of the leaderboard.
A three putt on the 17th then dropped him into the play-off at 14 under with playing partners McIlroy and Lorenzo Gagli, Andres Romero and Kalle Samooja as we went to extra holes at Crans-sur-Sierre Golf club for the sixth time in seven years.
The 28-year-old holed a ten footer for birdie on the first trip back up the last and, with McIlroy and Samooja missing from closer range, the trophy was his.
It was a thrilling finish to an enthralling day as all the main contenders came to life in the closing stages to take the event to a record equalling 13th play-off in its history.
Victory for Soderberg comes in his 50th European Tour event after he came through the Qualifying School in 2016 and the European Challenge Tour last season.
He has two wins on the Challenge Tour but sat 120th on the Race to Dubai coming into this week after securing a top five on home soil at last week’s Scandinavian Invitation.
“It’s unbelievable,” he said. “I’ve dreamt of playing on the European Tour, even better doing it this way. I was in the lead, lost it, went into the play-off with Rory McIlroy among it.
“I was more nervous in the beginning than I was towards the back nine. Got on a good run and the ball kept going in. Just playing with Rory, so many people around, playing with a guy like that adds heat to it right away.
“I proved to myself that I can play out here. I didn’t really know that I was ready to win, I had a terrible start to the season and I felt like I was just trying to make my way into the top 110 and keep my card for next year. It’s just a surreal way to do it.”
Soderberg bogeyed the first and birdied the driveable seventh to turn in 35 but it was a chip-in at the tenth that ignited his charge.
He holed long putts at the 11th and 12th and when he made another slippery one from distance on the 13th that sneaked in on the right side, he held the solo lead.
Samooja was not in the mood to be outdone and – after also bogeying the first – the Finn birdied the eighth and ninth and holed two long putts of his own on the 12th and 13th to get into a share, before Soderberg edged back ahead as he got up and down from sand on the 14th.
McIlroy was seeking redemption after bogeying the last and losing a play-off at this event in his rookie season 11 years ago but he looked a long way from making extra holes at two over for his round after ten.
The Northern Irishman birdied the 12th and 13th to get back to level and then took advantage of the back to back par fives at the 14th and 15th but he was still two behind.
A slippery right to lefter on the 17th had him within one and Gagli was also at 14 under when he followed him in after an impressive run of his own.
The Italian had double bogeyed the first but birdied the fifth, sixth and tenth before dropping a shot on the 11th. He then made the most of the 15th and almost aced the 16th, joining a four man tie when Soderberg three putted the next from ten feet.
Overnight leader Romero tumbled down the leaderboard as he bogeyed the first, third and fifth and he was still three over for his round before he made the most of the back nine’s pair of par fives.
An approach to tap-in range at the 17th then put him in the play-off but he missed the green with his second as Gagli found the water on the trip back up the 18th, leaving the other three players over their birdie putts for the dramatic finale.
Spain’s Adri Arnaus fired a 64 to finish a shot out of the play-off alongside Frenchman Mike-Lorenzo Vera, one shot clear of Australians Lucas Herbert and Wade Ormsby, Englishman Tommy Fleetwood and Austrian Matthias Schwab.