The answer to this question is “no,” but that needs to be clarified and hedged a little bit. What I mean by “no” is that the Allies did not win the war because they had technology that was superior to that of the Axis. They did win the war because they were able to create more technology and because they chose to use their technology in ways that may have been superior to the ways in which the Axis used their technology.
The one major criticism of this argument would be that the atomic bomb had a fundamental role in the war. This was clearly a superior technology. However, I would argue that the US was going to win the war in the Pacific with or without the atomic bomb so the bomb could not have had a fundamental impact on the war.
We can argue that two things won the war. First, the Allies simply had more equipment. With the United States and the Soviet Union on their side, they could crank out huge quantities of equipment in factories beyond the reach of Axis bombers. This had a fundamental impact on the war as the Allies simply overwhelmed the Axis. Second, the Allies arguably used their technology better. The Germans, for example, decided not to produce any heavy bombers like the B-17. If they had such bombers, they might have devastated England much more effectively during the Blitz. As another example, instead of concentrating hard on getting jet fighters produced in large numbers (that would have been a truly superior technology), they squandered resources on things like the V-1 and V-2. So, the Allies arguably made better use of the technology they had.
In these ways, technology did not play a fundamental role in the outcome of the war.