We demonstrate that dissociative ionization of H_{2} can be fully manipulated in an angle-time-resolved fashion, employing a polarization-skewed (PS) laser pulse in which the polarization vector rotates. The leading and falling edges of the PS laser pulse, characterized by unfolded field polarization, trigger, sequentially, parallel and perpendicular transitions of stretching H_{2} molecules, respectively. These transitions result in counterintuitive proton ejections that deviate significantly from the laser polarization directions. Our findings demonstrate that the reaction pathways can be controlled through fine-tuning the time-dependent polarization of the PS laser pulse. The experimental results are well reproduced using an intuitive wave-packet surface propagation simulation method. This research highlights the potential of PS laser pulses as powerful tweezers to resolve and manipulate complex laser-molecule interactions.