Ingram made 101 not out off 47 balls and, although Wright later matched his score, Glamorgan won by 18 runs.
Colin Ackermann hit a six off the final ball as Leicestershire edged out Lancashire in a thrilling finish.
Surrey beat Somerset despite a 12-run over-rate penalty and there were also wins for holders Northants and Kent.
A total of 66 sixes were struck in Sunday's five games, 19 of them in the Sussex v Glamorgan game.
While South Africa's Test team crashed to a 211-run defeat against England at Lord's, it was a good day for some of their compatriots on the county circuit - especially those playing for Glamorgan.
Chief among them was Ingram, who hit seven sixes to rescue his side from 7-2. He added 130 with former Proteas batsman Jacques Rudolph (49) and then 70 off the final six overs with Johannesburg-born Chris Cooke (37 not out) as they posted 198-3.
When it was Glamorgan's turn to field, Ingram weighed in with the wickets of Ross Taylor and Ben Brown. And although Wright equalled Ingram's sixes tally in his 101 off 53 balls, he fell to another South African, Marchant de Lange, in the penultimate over as they came up short on 180-6.
At Aigburth, Liam Livingstone (48 off 34 balls) and Jos Buttler (39 off 21) were the main contributors to Lancashire Lightning's 173-9.
Leicestershire looked comfortable needing only six off the final over, but Mathew Pillans was run out after four singles to start the over.
Ackermann was on strike for the final ball from Kyle Jarvis and managed to clear the rope at deep extra cover to finish with an unbeaten 62 off 41 balls as they won by three wickets.
"In T20 cricket you have to come in with good intent, to hit the ball and to run hard," he told BBC Radio Leicester.
Somerset looked dead and buried against Surrey at The Oval as they were reduced to 82-7 after Arran Finch's 61 off 42 balls led the home side to 181-7.
But Surrey had reckoned without New Zealander Corey Anderson, who raced to a 30-ball half-century - and a decision by the umpires to award 12 penalty runs to the visitors because of their poor over-rate.
Somerset needed 12 to win off the last over, but Anderson was run out for 81 - and innings featuring seven sixes - and Surrey scraped home by four runs.
"They said we were tight, but I certainly was trying to do everything I could (to keep the rate up)," Surrey skipper Jade Dernbach told BBC Radio London.
"The other night, being on TV, there seemed to be a different kind of timekeeping taking place compared to this game. I'd like to see some consistency from a captain's point of view, so we know we're at. But we still got over the line and that's the most important thing."
Essex import Mohammed Amir came in for some rough treatment from the Kent batsmen at Beckenham, with Joe Denly hitting three sixes and a four in his second over as they tried to defend a score of 166-8.
Denly (32) and Sam Northeast (33) were removed by spinner Simon Harmer (2-21), but unlike the final over of the Essex innings in which three wickets fell, Kent opener Daniel Bell-Drummond saw his side home with a six off Amir, whose 3.3 overs cost 41 runs.
Bell-Drummond was 90 not out as Kent reached 169-3 with nine balls to spare, having struck four sixes and eight fours.
At Chester-le-Street, South Africans Rory Kleinveldt (3-28) and Tabraiz Shamsi (2-20) helped Northants restrict Durham Jets to 161-7, despite an unbeaten 53 by Jack Burnham.
Ben Duckett's 72 off 56 balls put them in control of their run-chase and a boundary by Rob Keogh (20 not out) saw them home with four balls to spare.
Tuesday
Northamptonshire v Yorkshire - Northampton (18.30 BST)
Wednesday
Sussex v Hampshire - Hove (18:30 BST)
Thursday
Gloucestershire v Kent - Cheltenham (14:30 BST)
Middlesex v Surrey - Lord's (18:15 BST)
Essex v Somerset - Chelmsford (19:00 BST)
Glamorgan's Colin Ingram and Luke Wright of Sussex hit the first T20 Blast centuries of the summer in a high-scoring clash at Arundel.