The Serb broke Almagro's serve three times in the opening set and then created the only break of the second - crucially at four games apiece – to claim victory after an hour and a half of action in California.
Almagro’s ambitious style, fierce serve and crisp forehands eventually proved little match for Djokovic, who contained the Spaniard’s game and picked his moments.
And a combination of frequent unforced errors and Djokovic’s superb returns led to the end of the road for the world number 12, who nonetheless will be proud of his finest-ever run in the desert tournament.
"It was always going to be a tough match," Australian Open champion Djokovic said after reaching the last four for a fourth time at Indian Wells.
"Almagro is an established top-10 player.
"What made me very happy and satisfied with my game today was my serving," added the Serb, who fired down five aces and won 73 percent of his second serve points.
"When I had chances, I used them."
Djokovic will now meet American John Isner in the semis.
Though Almagro began confidently enough in service, it was not long before inconsistency reared its ugly head and Djokovic took advantage for the first break of the match to go three games to one ahead.
The Spanish player impressed by breaking right back – the first time in his career he had done so against Djokovic – but once again conceded a service game immediately following before the top seed made it 5-2 in just one minute and two seconds.
The strength of Almagro’s forehand won him game eight, yet only delayed the inevitable as Djokovic’s third love-service game put him one set up.
The 12th seed shored up his all-round game to stay toe-to-toe with his opponent for much of the second set, showing a steely nerve to claim the seventh advantage point of a 12-minute game to go 4-3 ahead - but that would be his last game of the match.
Though Almagro clawed back from three game points to force deuce, he was unable to break Djokovic’s serve at a potentially vital time in his quest to force a third set - and the Serb then did just that in the next game with some slick backhand play.
Serving for the match, the current best player in the world once again struck without reply in short order, sealing the first of three quarter-final points with another deft backhand.
This was far from Djokovic at his very best, though considering the erratic-yet-entertaining style of his opponent, a calm and authoritative display proved enough to prevent an upset.