Muller's 14 goals in 10 matches at the 1970 and 1974 finals remained a record until he was passed by Brazil's Ronaldo in Germany four years ago, and explain why the man known simply as 'Der Bomber' struck fear into opponents.
His extraordinary goalscoring record says it all: 68 goals in 62 appearances for West Germany, 365 in 628 for Bayern Munich.
Short and stocky with powerful thighs, Muller's build gave him explosive speed over short distances and the ability to shoot at goal with frightening velocity.
His low centre of gravity also enabled him to twist and turn his body quickly, allowing him to convert unlikely openings into goals.
"I have this instinct for knowing when a defence is going to relax, or when a defender will make a mistake," Muller once said when asked to explain his gifts. "Something inside me says, 'Gerd go this way; Gerd go that way'. I don't know what it is."
Born in 1945, Muller's career might never have got off the ground had he heeded the advice of a coach at Munich club TSV while working in a textile mill as a teenager.
"You won't go far in soccer," the young Muller was told. "Better try something else."
The coaches of Bayern Munich knew quality when they saw it however, and Muller was signed in 1964, quickly establishing himself as a goalscorer par excellence.
In October 1966 Muller was handed his international debut, launching a career that would see him finish as his country's record goalscorer.
When he arrived at the 1970 Mexico finals he was scoring at a rate of close to one a game, and his prowess was confirmed when he finished the tournament as top scorer after netting 10 goals in six appearances.
Among his goals in Mexico was his hooked close-range volley in the 3-2 extra-time victory over England in the quarter-finals, a poacher's finish that was to become Muller's calling card.
Though Muller's scoring feats for the Germans in Mexico were not enough to help his team beyond the semi-finals, he was to prove just as lethally effective on home soil at the 1974 World Cup.
His four-goal haul might not have been anything like that of four years earlier, but among his efforts in Germany was the most important strike of his career - the winner against Holland in the final.
Having clawed their way back into the match after favourites Holland had taken an early 1-0 lead, Muller was on hand to put West Germany 2-1 ahead shortly before half-time.
It was a goal that owed everything to Muller's fabled ability to create something out of nothing. Rainer Bonhof crossed low from the right flank and the ever-alert Muller reacted quickest.
His first touch nudged the ball away from the Dutch goal, but with his second he changed his body position sharply and connected with a low right-foot finish past Jan Jongbloed.
The 1974 final was Muller's last match for West Germany, though he continued playing until 1978 before a short spell in the United States.
