Dimensional regularization, that is compute in “4 + ε space-time dimensions” and take the limit ε→0 at the end, is a powerful tool in quantum field theory. In fact, Veltman and ’t Hooft won the 1999 Physics Nobel Prize, for dimensional regularization and its application to Yang-Mills theory. The work of Veltman and ‘t Hooft dates back to 1971 and was published in 1972 .
However, the original idea may have come from two physicist working in Argentina. According to Wolfgang Bietenholz & Lilian Prado, it was Juan Jose Giambiagi and Carlos Guido Bollini  in a paper submitted before Veltman and ‘t Hooft, who first proposed dimensional regularization .
The paper of Giambiagi and Bollini, although submitted for publication earlier, was actually published after the paper of Veltman and ‘t Hooft.
Juan José Giambiagi (1924 – 1996)
Read the short preprint by Bietenholz & Prado, which is available on the arXiv, for more details.
Carlos Guido Bollini
Wolfgang Bietenholz & Lilian Prado,40 Years of Calculus in 4 + epsilon Dimensions,(2012) arXiv:1211.1741v1 [physics.hist-ph]
C.G. Bollini and J.J. Giambiagi, Lowest order ‘divergent’ graphs in n-dimensional space, Phys. Lett. 40B (1972) 566-568.
 G. ’t Hooft & M. Veltman, Regularization and renormalization of gauge fields Nucl. Phys. B44 (1972) 189-213.