Using 448.1 $times$ $10^{6}$ $psi(3686)$ events collected with the BESIII detector at BEPCII, we employ a single-baryon tagging technique to make the first observation of $psi(3686)rightarrowXi(1530)^{-}barXi(1530)^{+}$ and $Xi(1530)^{-}barXi^{+}$ decays with a statistical significance of more than 10$sigma$ and 5.0$sigma$, respectively. The branching fractions are measured to be $cal{B}$$[psi(3686)rightarrowXi(1530)^{-}barXi(1530)^{+}] $ = (11.45 $pm$ 0.40 $pm$ 0.59) $times$ $10^{-5}$ and $cal{B}$$[psi(3686)rightarrowXi(1530)^{-}barXi^{+}]$ = (0.70 $pm$ 0.11 $pm$ 0.04) $times$ $10^{-5}$. The angular distribution parameter for $psi(3686)rightarrowXi(1530)^{-}barXi(1530)^{+}$ is determined to be $alpha$ = 0.40 $pm$ 0.24 $pm$ 0.06, which agrees with the theoretical predictions within 1$sigma$. The first uncertainties are statistical, and the second systematic.
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