Orr was superbly supported by Tom Alsop and Mohammad Rizwan, who made 55 and 76 not out respectively, as Sussex chased down a target of 342 in 76 overs to win by five wickets with 17 balls to spare at Hove.
Orr was caught on the mid-wicket boundary when Sussex still needed 68, but Rizwan – making his last appearance for the county before returning to international duty with Pakistan – saw them home in relative comfort.
Surrey stunned by Sussex.
Orr said: "There are some young guys in our team who haven't been on the winning side for us in the Championship so to win that is a very special feeling after four hard days, everyone in our dressing room is so happy.
"When they pulled out this morning after the rain we had a feeling we could win. It spun a bit but it's been a good wicket throughout and we believed in ourselves.
"The small boundary on one side was very appealing, and when the spinners came on or if they dropped it short I was always going to target it and luckily I managed to get a few runs that way. Having Mohammad Rizwan at the other end took all the pressure off towards the end, even when I got out, he was so calm and had the chase under control. Hopefully this is a springboard for us. It's massive for our confidence for the rest of the season, something for us to build on."
Having had a first-innings lead of 214 just before tea on the third day Derbyshire will wonder how they lost the game.
But after electing not to enforce the follow-on they surrendered seven wickets in adding 127 to their lead on the third day and they were unable to bat Sussex out of the game by adding quick runs in the morning session today after 14 overs were lost to rain and the start delayed until 12.15pm.
But that should not take away from Sussex’s achievement, and in particular the performance of left-hander Orr, who hit 15 fours and six sixes as he punished the bowlers every time they erred in line or length. It was an outstanding innings by the 21-year-old.
After skipper Tom Haines was lbw to the fourth ball from off-spinner Alex Thomson, having put on 47 for the first wicket, Orr and Alsop ticked along comfortably through the afternoon session and were always up with the asking rate of 4.5 runs an over.
They crucially picked up the tempo in some style in the four overs before tea by plundering 45 runs with Orr taking 17 off an over from Sam Conners before Alsop hit two sixes and two fours in striking Thomson for 20.
They added 140 in 36 overs with Alsop contributing 55, including six fours and two sixes, before he miscued a drive to mid-off off Anuj Dal shortly after tea.
But Rizwan immediately got into one-day mode as he picked up the tempo and the Derbyshire attack struggled to defend the short boundary on the scoreboard side. They weren’t helped, either, by no fewer than six ball changes.
Although Rizwan was hampered by what looked like a hamstring injury shortly after reaching his fifty, he always had the chase under control, even when Orr departed to a standing ovation after he was caught on the mid-wicket boundary off Luis Reece, having faced 203 balls and batted for a shade under four hours.
Cameos from Delray Rawlins and Ollie Carter made sure Sussex didn’t lose their way and Rizwan was unbeaten on 76 from 80 balls, with a six and nine fours, when Dan Ibrahim hit the winning boundary and Sussex could celebrate.