The first observation of the decays ¯¯¯B0s→D+sK−π+π− and ¯¯¯B0→D+sK−π+π− are reported using an integrated luminosity of 1.0  fb−1 recorded by the LHCb experiment. The branching fractions, normalized with respect to ¯¯¯B0s→D+sπ−π+π− and ¯¯¯B0s→D+sK−π+π−, respectively, are measured to be B(¯¯¯B0s→D+sK−π+π−)B(¯¯¯B0s→D+sπ−π+π−)=(5.2±0.5±0.3)×10−2 and B(¯¯¯B0→D+sK−π+π−)B(¯¯¯B0s→D+sK−π+π−)=0.54±0.07±0.07, where the first uncertainty is statistical and the second is systematic. The ¯¯¯B0s→D+sK−π+π− decay is of particular interest as it can be used to measure the weak phase γ. First observation of the ¯¯¯B0s→Ds1(2536)+π−, D+s1→D+sπ−π+ decay is also presented, and its branching fraction relative to ¯¯¯B0s→D+sπ−π+π− is found to be B(¯¯¯B0s→Ds1(2536)+π−,D+s1→D+sπ−π+)B(¯¯¯B0s→D+sπ−π+π−)=(4.0±1.0±0.4)×10−3.