Haas, who turns 35 on April 3, needed just 80 minutes to register his second victory over a world number one, following his upset victory against Andre Agassi in the quarter-finals of the 1999 Grand Slam Cup.
Tuesday's defeat snapped Djokovic's 14-match winning streak in the tournament as the Australian Open champion lost for just the second time this season.
The victory carried Haas into the Miami quarter-finals for the first time while he improved his head-to-head record against Djokovic to 3-4.
World number three Murray, seeded second in Miami in the absence of Roger Federer, had none of the troubles he had suffered in the previous round against Grigor Dimitrov and booked his place in the last eight with a 6-2 6-4 win over Seppi in just 86 minutes.
Every time Murray has won his first match in Miami, he has reached the semi-finals or better, but he will have to beat ninth seed Marin Cilic if he is to repeat that feat again this year. The Croat produced an assured performance to beat sixth-seeded Jo-Wilfried Tsonga 7-5 7-6(3).
Murray made a confident start to the match but was helped by a nervy start from Seppi, who failed to find a first serve in the opening game, instead handing the break to the Scot.
The 25-year-old eased through each of his service holds before breaking again in the seventh game, pummelling the Seppi forehand which eventually broke down, and then serving out the set with little trouble.
Seppi cut a much more confident figure in the second set as he pushed Murray harder on the Scot's serve. Still the Italian could not fashion himself a break point though and it was Murray who again made the breakthrough, this time in the ninth game, when Seppi netted forehands on three consecutive points.
Murray did have a little trouble serving for the match, handing Seppi a break back point with a double fault.
But it was only a momentary wobble from Murray as he saved the break point with an ace down the centre of the court before wrapping up the win when Seppi sent a forehand long.
Nishikori caused Ferrer just the one moment of real concern when he broke as the Spaniard served for the first set.
Ferrer lost his temper with a linesman who had called a ball out only to correct himself, thereby forcing the rally to be replayed. The Spaniard lost the replay - and the game - and went on to demand that the linesman be removed during the change of ends.
The request was refused and Ferrer recovered his composure in enough time to break in the very next game to seal the set, before easing through the second set.
Ferrer will next face Juergen Melzer, the Austrian forced to come back from a set down to beat Spaniard Albert Ramos 2-6 6-3 6-3.
Miami Masters results
15-Tommy Haas (Germany) beat 1-Novak Djokovic (Serbia) 6-2 6-4
11-Gilles Simon (France) beat 7-Janko Tipsarevic (Serbia) 5-7 6-2 6-2
9-Marin Cilic (Croatia) beat 6-Jo-Wilfried Tsonga (France) 7-5 7-6(4)
4-Tomas Berdych (Czech Republic) beat 17-Sam Querrey (U.S.) 6-1 6-1
2-Andy Murray (Britain) beat 16-Andreas Seppi (Italy) 6-2 6-4
8-Richard Gasquet (France) beat 10-Nicolas Almagro (Spain) 6-7(3) 7-5 7-6(3)
Jurgen Melzer (Austria) beat Albert Ramos (Spain) 2-6 6-3 6-3
3-David Ferrer (Spain) beat 13-Kei Nishikori (Japan) 6-4 6-2
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