By the time the MS670 appeared, Matra had spent the better part of six years developing endurance racing hardware, moving progressively through the MS620, MS630, MS650, and MS660 families. Each generation had extracted more from the team's 3.0-litre V12 engine while refining the chassis and aerodynamics. The MS670 represented the culmination of that process: a car efficient enough, reliable enough, and fast enough to compete for overall victory at Le Mans against the most powerful opposition of the era.
The MS670 made a single competitive appearance in 1972, at the 24 Hours of Le Mans. Matra entered four cars. Jean-Pierre Beltoise and Chris Amon drove the older MS660C, while the three MS670 entries were for François Cevert and Howden Ganley, Henri Pescarolo and Graham Hill, and Jean-Pierre Jabouille and David Hobbs.
Hill and Pescarolo won the race by a lap from Cevert and Ganley. Beltoise and Amon retired with engine failure, and Jabouille and Hobbs retired with a broken gearbox. The victory was Matra's first at Le Mans and came at the first attempt with the MS670. In the World Championship for Makes, Matra scored twenty points, finishing seventh in the championship — a result reflecting the limited number of rounds they contested.
For 1973 an updated MS670B was introduced from the Vallelunga 6 Hours onward. Matra opened the year at the 24 Hours of Daytona using the original MS670, with Cevert, Beltoise, and Pescarolo sharing a single entry, which retired with engine failure.
The MS670B's debut came at the Vallelunga 6 Hours. Cevert, Pescarolo, and Gérard Larrousse won the race together; a second entry for Cevert and Beltoise retired with engine failure. The pairing of Pescarolo and Larrousse quickly established itself as Matra's primary attack. At the 1000 km of Dijon they won outright, with Cevert and Beltoise third. At the 1000 km of Monza, Pescarolo and Larrousse finished third and Cevert and Beltoise eleventh. At the 1000 km of Spa, a three-driver entry of Pescarolo, Larrousse, and Chris Amon finished third, while a pairing of Pescarolo, Amon, and Graham Hill retired with engine failure. Both Matra cars retired at the 1000 km of Nürburgring with engine failures.
At the 24 Hours of Le Mans, Matra entered four cars. Pescarolo and Larrousse won the race, with Jabouille and Jean-Pierre Jaussaud finishing third. Cevert and Beltoise retired after an accident caused by a puncture, and Patrick Depailler and Bob Wollek retired with a broken oil pump compounded by engine failure. The 1000 km of Zeltweg brought Pescarolo and Larrousse their fourth victory of the season, ahead of Cevert and Beltoise. The final round, the Watkins Glen 6 Hours, saw Pescarolo and Larrousse win again, while Cevert and Beltoise retired with a broken ignition.
Matra accumulated 124 points in 1973, winning the World Championship for Makes.
The MS670C debuted at the 1974 1000 km of Monza, where both Matra entries — Pescarolo and Larrousse, and Jean-Pierre Beltoise with Jean-Pierre Jarier — retired with engine failure. The team found its rhythm quickly thereafter. Jarier and Jacky Ickx won the 1000 km of Spa; Pescarolo and Larrousse retired from that race with a broken head gasket. At the 1000 km of Nürburgring, Beltoise and Jarier won, with Pescarolo and Larrousse fifth. Pescarolo and Larrousse won the 1000 km of Imola, with Beltoise and Jarier fourth.
Matra ran the new MS680 at Le Mans rather than the MS670C. Pescarolo and Larrousse won that race for the third consecutive year, with Jabouille and François Migault finishing third. After Le Mans the team reverted to the MS670C for the remainder of the season. Pescarolo and Larrousse won the 1000 km of Zeltweg with Beltoise and Jarier third. Beltoise and Jarier won the Watkins Glen 6 Hours, the 1000 km of Le Castellet, and the 1000 km of Brands Hatch, with Pescarolo and Larrousse second in all three. At the final round, the Kyalami 6 Hours, Pescarolo and Larrousse won from Beltoise and Jarier.
Matra scored 140 points in 1974, winning the World Championship for Makes for the second consecutive season. At the end of the year, Matra withdrew from motor racing entirely.
The MS670 family delivered one of the most dominant three-year runs in World Championship for Makes history: three consecutive Le Mans victories, two consecutive manufacturers' titles, and a record of race wins across venues as varied as Dijon, Spa, Nürburgring, Zeltweg, Watkins Glen, Le Castellet, Brands Hatch, and Kyalami. The Pescarolo and Larrousse pairing became the most successful combination of the era within the series. Matra's withdrawal after 1974 left a vacuum at the top of prototype racing that other manufacturers rushed to fill in the years that followed.