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We present the first characterisation of the average dust attenuation curve at $z\sim1.3$ by combining rest-frame ultraviolet through near-IR photometry with Balmer decrement ($\mathrm{H}α$/$\mathrm{H}β$) constraints for $\sim$900 galaxies with $8\lesssim\log (M_\star /M_\odot)<10.2$ at $0.75<z<1.5$ in the HST WFC3 IR Spectroscopic Parallel (WISP) and 3D-HST grism surveys. Using galaxies in SDSS, we establish that the ($\mathrm{H}α$+[NII])/[OIII] line ratio and stellar mass are good proxies for the Balmer decrement in low-spectral resolution grism data when only upper-limits on $\mathrm{H}β$ are available and/or $\mathrm{H}α$ is blended with [NII]. The slope of the $z\sim1.3$ attenuation curve ($A(0.15μm)/A(V)=3.15$) and its normalization ($R_V=3.26$) lie in-between the values found for $z=0$ and $z\sim2$ dust attenuation curves derived with similar methods. These provide supporting evidence that the average dust attenuation curve of star forming galaxies evolves continuously with redshift. The $z\sim1.3$ curve has a mild 2175Å feature (bump amplitude, $E_b=0.83$; $\sim$25% that of the MW extinction curve), which is comparable to several other studies at $0<z\lesssim3$, and suggests that the average strength of this feature may not evolve significantly with redshift. The methods we develop to constrain dust attenuation from HST grism data can be applied to future grism surveys with JWST, Euclid, and RST. These new facilities will detect millions of emission line galaxies and offer the opportunity to significantly improve our understanding of how and why dust attenuation curves evolve.