K2-146 is a cool, 0.358M_{sun}_ dwarf that was found to host a mini-Neptune with a 2.67day period. The planet exhibited strong transit timing variations (TTVs) of greater than 30minutes, indicative of the presence of an additional object in the system. Here we report the discovery of the previously undetected outer planet in the system, K2-146c, using additional photometric data. K2-146c was found to have a grazing transit geometry and a 3.97day period. The outer planet was only significantly detected in the latter K2 campaigns presumably because of precession of its orbital plane. The TTVs of K2-146b and c were measured using observations spanning a baseline of almost 1200days. We found strong anti-correlation in the TTVs, suggesting the two planets are gravitationally interacting. Our TTV and transit model analyses revealed that K2-146b has a radius of 2.25{+/-}0.10R_{earth}_ and a mass of 5.6{+/-}0.7M_{earth}_, whereas K2-146c has a radius of 2.59_-0.39_^+1.81^R_{earth} and a mass of 7.1{+/-}0.9M_{earth}_. The inner and outer planets likely have moderate eccentricities of e=0.14{+/-}0.07 and 0.16{+/-}0.07, respectively. Long-term numerical integrations of the two-planet orbital solution show that it can be dynamically stable for at least 2Myr. We show that the resonance angles of the planet pair are librating, which may be an indication that K2-146b and c are in a 3:2 mean motion resonance. The orbital architecture of the system points to a possible convergent migration origin. Description : The K2 photometric observations were obtained between 2015 April 27 and 2018 July 2, spanning a baseline of almost 1200 days. The K2 target pixel data were downloaded from the Mikulski Archive for Space Telescope (MAST). We obtained spectra with the Habitable-zone Planet Finder (HPF) between 2019 February 22 and 2019 May 9. HPF is a high-resolution (R=55000) precision-fiber-fed, near-infrared (NIR) spectrograph recently installed on the Hobby-Eberly Telescope, covering the information-rich z, Y, and J bands (810-1280 nm). The methods used to extract the transit times is describe in section 4 of the article.