The production Riviera shared its bodyshell with no other model, which was unusual for a GM product. It rode a cruciform frame similar to the standard Buick frame, but shorter and narrower, with a 2.0 in (51 mm) narrower track. Its wheelbase of 117 in (3,000 mm) and overall length of 208 in (5,300 mm) were 6.0 inches (150 mm) and 7.7 in (200 mm) shorter, respectively, than a Buick LeSabre, but slightly longer than a contemporary Thunderbird. At 3,998 lb (1,813 kg), it was about 390 pounds (180 kg) lighter than either. It shared the standard Buick V8 engines, with a displacement of either 401 cu in (6.57 L) or 425 cu in (6.96 l), and Twin Turbine automatic transmission. Brakes were Buick's standard "Al-Fin" (aluminum finned) drums of 12 in (300 mm) diameter. Power steering was standard equipment, with an overall steering ratio of 20.5:1, giving 3.5 turns lock-to-lock.
The Riviera's suspension used the same basic design as standard Buicks, with double wishbones front and a live axle located by trailing arms and a lateral track bar, but the roll centers were raised to reduce body lean. Although its coil springs were actually slightly softer than other Buicks, with the lighter overall weight, the net effect was to make the Riviera somewhat firmer. Although still biased towards understeer, contemporary testers considered it one of the most roadable American cars, with an excellent balance of comfort and agility.
The Riviera was introduced on October 4, 1962 as a 1963 model, with the 325 hp (242 kW) 401 cu in (6.6 l) as the only available engine and the Turbine Drive the only transmission, at a base price of $4,333; typical delivered prices with options ran upwards of $5,000. Production was deliberately limited to 40,000 or less to increase demand.
With the same power as the larger Buicks and less weight, the Riviera had sparkling all-around performance: Motor Trend found it capable of running 0–60 mph (0–97 km/h) in 8 seconds or less, the standing quarter mile in about 16 seconds, and an observed top speed of 115 miles per hour (185 km/h), although 125 miles per hour (201 km/h) was feasible with a longer run. Fuel economy was a meager 13.2 miles per US gallon (17.8 L/100 km; 15.9 mpg-imp).
Inside, the Riviera featured a four-place cabin with front bucket seats separated by a center console with floor shifter and storage compartment that was built into the instrument panel, and bucket-style seats in the rear. Upholstery choices included all-vinyl, cloth and vinyl, or optional leather. Popular extra-cost options included a tilt steering wheel, cruise control, power windows, power seats, air conditioning, AM/FM radio, and wire wheel covers.
The Riviera continued with minimal trim changes for 1964 including the discontinuation of leather upholstery from the option list, differing mainly in substitution of the old two-speed Dynaflow-based Twin Turbine for the new three-speed Super Turbine 400, which was marketed as Turbo Hydra-Matic by other GM divisions. This was the first year that the Stylized "R" emblem was used on the Riviera, a trademark that would continue throughout the remainder of Riviera's 36-year production run. Under the hood, the 401 cu in (6.6 l) was dropped in favor of the 340 hp (254 kW) 425 cu in (7.0 l) V8. A 'Super Wildcat' version was optionally available, with dual Carter AFB four-barrel carburetors, rated at 360 hp (268 kW).
Changes for 1965 included the introduction of the Gran Sport option, which included the dual-quad Super Wildcat 425 V8, a numerically higher 3.42 axle ratio, dual exhausts, and stiffer, heavy-duty suspension. The 401 cu in (6.6 l) V8 returned as the standard Riviera engine and the Super Turbine 400 transmission now had a variable pitch torque converter like the old Twin Turbine Dynaflow had two years before. Externally, the headlamps were concealed behind clamshell doors in the leading edges of each fender, as in the original design. Further back, the non-functional side scoops between the doors and rear wheel arches were removed, and the taillights were moved from the body into the rear bumper. A vinyl roof became available as an option, initially offered only in black, and the tilt steering wheel optional in previous years was now standard equipment.
Total sales for the three model years was a respectable 112,244. All in all, the Riviera was extremely well-received and considered a great success, giving the Thunderbird its first real competition.