We present results from a multi-wavelength campaign to monitor the 2005 outburst of the low-mass young star V1118 Ori. Although our campaign covers the X-ray, optical, infrared, and radio regimes, we focus in this Letter on the properties of the X-ray emission in V1118 Ori during the first few months after the optical outburst. Chandra and XMM-Newton detected V1118 Ori at three epochs in early 2005. The X-ray flux and luminosity stayed similar within a factor of two, and at the same level as in a pre-outburst observation in 2002. The hydrogen column density showed no evidence for variation from its modest pre-outburst value of $N_\mathrm{H} \sim 3 \times 10^{21}$ cm$^{-2}$. However, a spectral change occurred from a dominant hot plasma ($\sim 25$ MK) in 2002 and in January 2005 to a cooler plasma ($\sim 8$ MK) in February 2005 and in March 2005. We hypothesize that the hot magnetic loops high in the corona were disrupted by the closing in of the accretion disk due to the increased accretion rate during the outburst, whereas the lower cooler loops were probably less affected and became the dominant coronal component.