The Belarusian challenger was relentless in his pursuit of the 33-year-old Scot in Glasgow but lost a superb battle unanimously on points.
Burns made the most of his greater experience to try to quell Relikh, 26.
"Boy, he could whack," remarked Burns, who now hopes to finalise a fight against America's Adrien Broner.
"There were a couple of times when he shook me with body shots and head shots, but I managed to hide it from him and I stuck to my tactics and stayed on my bike."
Broner had intimated that he would be ringside but did not travel across the Atlantic to assess Burns at close quarters.
Burns' winning margin seemed generous, with one judge scoring the bout 118-110 and another two putting it, more accurately, at 116-112.
Previously unbeaten Relikh, trained by Ricky Hatton and based in Manchester, began in a lively fashion, evidently enjoying the challenge.
He chased Scotland's first three-weight world champion around the ring and succeeded in landing some good shots to his ribs.
Even by round four, Burns, with 40 wins from 46 bouts prior to this bout, had to use his superior movement and many years of ringcraft to get himself out of tight spots and hope that his opponent would tire.
The fifth round offered signs that Burns was finding his range and, although the eager Relikh did not take a step backwards, the Scot scored with blows to the chin.
Relikh was becoming more ragged, but he maintained his work-rate with a series of assaults. However, despite the challenger having 19 knockouts in his 21 previous fights, it was Burns who looked the heavier hitter.
The pattern continued into the middle rounds as Burns kept his focus to jab away at Relikh and then try to hurt him with body shots.
The fight began to turn in Burns' favour by the eighth as he increased the tempo and connected strongly with his right.
Relikh had never fought beyond eight rounds and, in the ninth, perhaps becoming increasingly desperate, he threw his shoulder up into Burns' jaw and was reprimanded by the referee.
The 10th was the pick of the rounds. Relikh took two thumping shots to the jaw, but his aggression had not lessened and when he landed a big left he appeared to have Burns in trouble for the first time in the fight.
The final action was no less engaging with the SSE Hydro crowd roaring Burns on, enough to see him over the finishing line.
For Burns, a lucrative defence awaits. Relikh, surely, will fight for another world title.
"Fair play to him, he stuck at it for the full 12 rounds," said Burns. "He was still in there at the end. He'll definitely come again, he's a good fighter."
Britain's Ricky Burns was given a stern test as he made a successful first defence of his WBA world super-lightweight title against Kiryl Relikh.