Selby, who won the most recent ranking event at last month's English Open by beating Luca Brecel in the final, was comprehensively outgunned by his Thai opponent.
There were no signs of nerves at coming up against the world number two as Saengkham peeled off a 122 break to seal the opening frame before taking a scrappy second at The Centaur in Cheltenham.
His opponent, a four-time world champion, ate into the deficit with a 71 break but visits of 75 and 104 in the next two frames secured a shock win for Saengkham, who will face O'Sullivan next.
O'Sullivan was rarely troubled in a potentially tricky opener against Barry Hawkins, blowing away an opponent he beat in the World Championship final a decade ago.
The world number one did not look back after firing in a 108 break in the opener and he eventually strolled to a commanding 4-0 victory.
Trump, who beat Mark Williams 10-8 in a closely-contested Masters final last weekend, twice had to come from behind before defeating Hossein Vafaei.
Breaks of 91 and 68 - either side of Trump's 107 - put the Iranian 2-1 ahead but the Bristol potter drew level for a second time with a fantastic 138 clearance.
He won the next two frames and will face either Joe Perry or Brecel in round two.
Two days after his defeat in the Alexandra Palace showpiece, Williams got back to winning ways as the Welshman knocked in three ton-plus breaks to defeat Jamie Jones 4-1.
Williams will take on Ding Junhui next, with the Chinese closing out a 4-0 clean sweep of Stuart Bingham with a fine break of 133.
Kyren Wilson defeated Robbie Williams 4-2 and will next take on Shaun Murphy or Ali Carter while Joe O'Connor defeated China's Lyu Haotian by the same scoreline to book a clash against Mark Allen.