Tuilagi, whose brother Manu is on tour with the British and Irish Lions in Australia, gave an impressive exhibition of brute strength to power over for his two scores as Samoa snapped a streak of eight previous matches without success against the Scots.
Fullback James So'oialo got Samoa's other try and contributed 12 points from the boot.
Samoa's imposing pack and fast-paced backline ensured a storming start with two tries in the opening 13 minutes.
So'oialo opened the scoring in the seventh minute as Samoa fielded a Scottish kick inside their own half to set up a sweeping move, finished off by the fullback.
Tuilagi scored his first from the left wing six minutes later as the huge frames of the Samoans battered through the Scottish defence.
Indiscipline in the scrums allowed Scotland to keep in touch through the boot of scrumhalf Greig Laidlaw, who kicked four penalties but also missed two easy opportunities.
"We were always scrambling after conceding the first two tries," Laidlaw said. "We won't take too much out of today, we need to go and have a hard look at ourselves."
Scotland enjoyed a brief lead at 17-14 when they reaped the rewards of a period of sustained pressure early in the second half which led to Sean Lamont scoring on the right wing.
But they held the advantage for only a few minutes before So'oialo kicked over a penalty for parity, followed by Tuliagi's second try as he raced through the Scottish defence, brushing aside a tackler to dive between the posts in the 64th minute.
"We've always been on the wrong side of some close results against Scotland, so it's great to right that today," Samoa captain Paul Williams said.
Later on Saturday South Africa play Italy, while next weekend Scotland take on the Springboks and Samoa meet Italy.
A points table will determine the pairings of the four teams for a third round of tests in Pretoria on June 22.