Tony Southgate, a former BRM engineer, designed the DN3 as a direct development of the DN1 he had previously created for Shadow. The redesign focused on eliminating excessive vibration that had plagued the earlier car by stiffening the monocoque structure. The DN3 also featured a longer wheelbase than the DN1, though it was around five kilograms heavier as a result. Like its predecessor, it was powered by the ubiquitous Ford Cosworth DFV 3-litre V8 engine.
Shadow entered the 1974 championship with two drivers: Jean-Pierre Jarier and Peter Revson, who had joined the team after winning races for McLaren. Revson showed early promise with the DN3, qualifying fourth and sixth in the first two races of the year. However, he was killed in a testing accident before the South African Grand Prix, and Shadow was forced to withdraw from that event.
Brian Redman stepped in to replace Revson from the Spanish Grand Prix onwards, taking part in three races before Swedish driver Bertil Roos made a guest appearance at his home race in Sweden. Tom Pryce, who had made his Formula One debut earlier that year with the Token Racing team, then assumed the second seat for the remainder of the season.
Jarier continued as the team's lead driver throughout, and despite the personal blow of losing his teammate Revson, he delivered the season's highlight: a third-place finish at Monaco after qualifying sixth. He followed that up with fifth at the Swedish Grand Prix. Pryce contributed a sixth-place finish at the German Grand Prix, earning a single championship point. Shadow finished the 1974 Constructors' Championship in eighth place with seven points — six from Jarier and one from Pryce.
With the new Shadow DN5 not immediately available for both drivers at the start of 1975, Tom Pryce used an updated version of the chassis, designated DN3B, for the opening two races of the season. He did not score points with the older car, and the DN3B was retired from competition once the DN5 was ready.
The Shadow DN3 occupies a modest but notable place in mid-1970s Formula One history. It stabilised Shadow's technical direction after the troubled DN1 and gave the team its best result of that era in Jarier's Monaco podium. The car also served as a platform for Tom Pryce to break into Formula One at the senior level, launching a career that would show considerable promise before his tragic death at the 1977 South African Grand Prix. Southgate's methodical development approach with the DN3 laid the groundwork for later Shadow designs including the DN5, which carried the team to greater competitiveness in 1975.