The Namibian, unbeaten in 21 fights prior to Saturday's unification contest in Glasgow, forced his fellow 34-year-old onto the back foot for much of the fight.
For all of his efforts, the Scot was outshone by Indongo over 12 tough rounds, losing a unanimous decision of 120-108, 118-110, 116-112.
The 5'10" challenger, who was making just his second appearance outside of his homeland, was busy and confident from the start while Burns was cautious early on.
Burns, however, was never able to get into gear and failed to get to grips with the tall, energetic southpaw.
Indongo sent the champion stumbling across the ring after landing a looping left to the jaw in the fifth round as Burns was left with the task of making up a points deficit by the halfway point.
Burns showed more resolve in the sixth round but in the eighth he came close to be stopped when Indongo almost overwhelmed him, and ultimately, the result was never in doubt.