British number one Murray produced some thunderous groundstrokes to take the first set on a tie-breaker, but he fell apart at the start of the second to hand the initiative to his Argentinian opponent.
Although he finally created his first break points of the match in the third set, Murray could not convert and a raft of unforced errors - he made 49 overall - meant Del Potro won at a canter in the end, in two hours and 31 minutes.
This was the first time Murray had faced the Argentinian since beating him in 2009, but he survived a scare in the very first game in Indian Wells.
Del Potro had break points on the Murray serve, but the Scot fought back to deuce before serving out for a 1-0 lead.
Punishing baseline rallies were becoming the order of the day as the first set started to turn into a physical battle and Del Potro was forced to serve to stay in the set at 4-5 and 5-6 - which he did so with a little help from an errant Murray volley.
Third seed Murray threw away a two-mini-break advantage in the tie-breaker, but the Scot won a 43-shot rally on his opponent’s serve to bring up two set points and he converted at the second attempt.
Any thoughts Del Potro might wilt, though, soon disappeared as he won nine straight points at the start of the second, including a Murray double fault on break point, on his way to a three-game advantage.
Murray held to love to finally get on the board at 3-1, but he could make no impact on the Del Potro delivery and by the end of the second set, which Del Potro sealed with another dominant hold, had still not created a break point.
That changed in game two of the third set, but Murray could not handle a deep second serve to convert it, and a series of unforced errors in the next game allowed Del Potro three opportunities of his own, the third of which the Argentinian took.
Murray battled back from 40-15 down in game four, and the British number one brought up his second break point with a deep forehand, but again he could not convert.
Murray dumped another forehand into the net to hand Del Potro another break point in game five, then went long to give his opponent the double break, then a pair of double faults in his next service game completed what in the end was a comprehensive defeat.