Fluid invasion, displacement of one fluid by another in porous media, is important in a large number of industrial and natural processes. Of special interest is the trapping of gas and oil clusters. We study the impact of wettability on fluid pattern formation and capillary trapping in three‐dimensional glass beads packs (dmean = 1 mm) during fluid invasion at capillary numbers of 10−7 using μ‐CT. The invading fluid was water, and the defending fluid was air. The contact angle of the glass beads was altered between 5° and 115° using Piranha cleaning and silanization. We analyzed the front morphology of the invading fluid, the residual gas saturation, the fluid occupation frequency of pores, and the morphology and statistics of the trapped gas clusters. We found a sharp transition (crossover) at a critical contact angle θc = 96°. Below θc the morphology of the displacement front was flat and compact caused by the strong smoothing effect of cooperative filling. Above θc the morphology of the displacement front was fractal and ramified caused by single bursts (Haines jumps). Across this dynamical phase transition the trapping efficiency changes from no trapping to maximal trapping. For θ > θc the experimental results show that invasion percolation governs the fluid displacement. Strong indicators are the universal scaling behavior of the size distribution of large clusters (relative data error εdata < 1%) and their linear surface‐volume relationship (R2 = 0.99). Key Points Wettability‐controlled dynamical phase transition in trapping efficiency for 3‐D porous media (1‐mm glass beads) Trapping efficiency changes from no trapping to maximal trapping: Above the critical contact angle θc smaller pores are occupied by gas For θ > θc the results show that invasion percolation governs the fluid displacement: universal scaling for the trapped gas clusters