A key ingredient to obtaining topological quantum devices is the ability to control topological states without modifying the underlying properties of the material that hosts them. It is well known that in heavy fermion metals physical properties can be much more readily tuned than in simple metals. Such correlated materials may also exhibit extreme signatures of nontrivial topology, as recently demonstrated for the Weyl-Kondo semimetal Ce3Bi4Pd3 [1, 2, 3]. What has remained open, however, is whether these topological states are essentially inert, or can also be influenced by external control parameters. Here we show the latter to be the case: the material’s Weyl signatures can be fully suppressed by a relatively modest magnetic field [4]. We understand this behavior as a Zeeman-driven motion of Weyl nodes in momentum space, up to the point where the nodes meet and annihilate in a topological quantum phase transition. The topologically trivial but correlated background remains largely unaffected across this transition. Only at larger fields a transition from a correlated narrow-gap phase to a metallic heavy Fermi liquid phase is observed. Our work lies at the scarcely explored intersection between gapless topology and strong correlations, and accentuates the importance of materials innovation to obtain much needed breakthroughs in topological quantum applications. [1] S. Dzsaber et al., Phys.Rev. Lett. 118, 246601 (2017). [2] H. -H. Lai et al., Proc. Natl.Acad. Sci. U.S.A. 115, 93 (2018). [3] S. Dzsaber et al., Proc. Natl.Acad. Sci. U.S.A. 118, e2013386118 (2021). [4] S. Dzsaber et al., arXiv:1906.01182 (2019).