V.J. Katz in History of Topology:
Although Cartan realized that the three theorems of vector calculus (Gauss, Green, Stokes) could be easily stated using differential forms, it was Edouard Goursat (1858-1936) who in 1917 [1] first noted that these three theorems were all special cases of a generalised Stokes theorem for differential forms (first stated, in coordinate free form, by Volterra in 1889 [2]).
[1] E. Goursat, Sur certains systèmes d'équations aux différentielles totales et sur une généralisation du problème de Pfaff, Ann. Fac. Sci. Toulouse (3) 7 (1917), 1--58.
[2] V. Volterra, Sulle funzioni coniugate, Rendiconti Accademia dei Licei (4) 5 (1889), 599--611.