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The combined impact of a linear chemical reaction and Lorentz force on heat and mass transfer in a third-grade fluid with the Darcy–Forchheimer relation over an inclined, exponentially stretching surface embedded in a porous medium is investigated. The proposed process is mathematically expressed in terms of nonlinear and coupled partial differential equations, with the symmetry of the conditions normal to the surface. To solve the mathematical model of the proposed phenomenon, the partial differential equations are first reduced to ordinary differential equations; then, MATLAB built-in Numerical Solver bvp4c is used to obtain the numerical results of these equations. The influence of all the pertinent parameters that appeared in the flow model on the unknown material properties of interest is depicted in the forms of tables and graphs. The physical attitude of the unknown variables is discussed with physical reasoning. From the numerical solutions, it is inferred that, as Lorentz force parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>M</mi></semantics></math></inline-formula> is increased, the velocity of the fluid decreases, but fluid temperature and mass concentration increase. This is due to the fact that Lorentz force retards the motion of fluid, and the increasing resistive force causes the rise in the temperature of the fluid. It is also noted that, owing to an increase in the magnitude of chemical reaction parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>R</mi></semantics></math></inline-formula>, the velocity profile and the mass concentration decline as well, but the fluid temperature increases in a reasonable manner. It is noted that, by augmenting the values of the local inertial coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>r</mi></mrow></semantics></math></inline-formula> and the permeability parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>K</mi><mo>*</mo></msup></mrow></semantics></math></inline-formula>, the velocity field decreases, the temperature field increases, and mass concentration also increases with reasonable difference. Increasing values of Prandtl number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> results in a decrease in the profiles of velocity and temperature. All the numerical results are computed at the angle of inclination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>π</mi><mo>/</mo><mn>6</mn></mrow></semantics></math></inline-formula>. The current results are compared with the available results in the existing literature for this special case, and there is good agreement between them that shows the validation of the present study. All the numerical results show asymptotic behavior by satisfying the given boundary conditions.