Tebogo, 21, was able to ease up at the end and still clocked an African record of 19.46sec for gold with American Kenny Bednarek taking silver in 19.62sec and Lyles fading to bronze in 19.70sec.
The sole African to have won a short sprint title at an Olympic Games is South African Reggie Walker, over 100m at the 1908 Games in London.
His time saw him leapfrog American Erriyon Knighton to go fifth fastest in the all-time list. The gold was also Botswana's first ever at an Olympics.
"It was really a beautiful race for me," Tebogo said. "When we made it to the final, my coach just told me, 'Now my job is done, it's up to you to see what you can do. Whether it’s a medal or not, just finish the race healthy'.
"That's all I could've wished for. I'm happy I finished the race healthier than before."
Tebogo's gold is even more impressive given that he lost his mother Seratiwa in May. His running shoes bear his late mother's date of birth.
"It's basically me carrying her through every stride that I take inside the field," said the sprinter, who took a month off training and competition after her death.
"It gives me a lot of motivation. She's watching up there, and she's really, really happy. I didn't want to put the date of her death, because I'll get emotional."
Tebogo added: "I'm really grateful for the team around me. They really pushed me through thick and thin.
"We had our ups and downs, but we just made sure that we pulled through and made it to the Olympics."
The final lacked the pre-race hype of the 100m, falling mid-session at a packed Stade de France.
Lyles was given a huge reception when introduced as cameras showed him up on the big screens at either end of the stadium.
The newly crowned 100m champion was drawn in lane five, outside Alexander Ogando and inside American teammate Erriyon Knighton, while Tebogo was in seven.
The American bounded into the stadium, as he had done before the 100m final, cupping his ear to the crowd, but his exuberant showboating saw him yellow-carded for breaking the starting block.
Tebogo, however, walked quietly on and went straight to his blocks.
After the gun went for the start, Lyles was quickly up on Ogando.
He, Tebogo and Bednarek all rounded the bend well, but coming into the home straight, Lyles was in third spot.
But Tebogo looked in total control, even relaxing as he went through the finish line, making a brushing-off gesture to the rest of the field.
Bednarek held on for silver, with Lyles prone on the track after being unable to replicate his gold medal showing in the 100m.
