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We study the processes $pp \to t\bar{t}Z$ and $pp \to tZj$ in the framework of Standard Model Effective Field Theory (SMEFT), employing conventional cut-and-count as well as machine learning techniques to take advantage of kinematic information in complex final states involving multiple leptons and $b$ jets. We explore the projected sensitivity for two SMEFT operators, $\mathcal{O}_{tZ}$ and $\mathcal{O}_{tW}$, that induce electroweak dipole moment interactions for top quarks, through direct searches in these electroweak top production processes at the HL-LHC. New physics modifications to dominant backgrounds are also considered. We show that the new physics sensitivity can be enhanced through a combination of differential distributions for relevant kinematic observables and machine learning techniques. Searches in $t\bar{t}Z$ and $tZj$ production result in stronger constraints on $\mathcal{C}_{tZ}$ and $\mathcal{C}_{tW}$, respectively. At the HL-LHC, $\mathcal{C}_{tZ}$ can be probed up to $-0.41 \lesssim \mathcal{C}_{tZ} \lesssim 0.47$ through searches in the $pp \to t\bar{t}Z + tWZ \to 3\ell + 2b\ + \geq 2j$ channel while $\mathcal{C}_{tW}$ can be probed up to $-0.14 \lesssim \mathcal{C}_{tW} < 0.11$ from searches in the $pp \to tZj + t\bar{t}Z + tWZ \to 3\ell + 1b + 1/2j$ channel, at $95\%$ CL.