An i3 can be fine, if it's a more recent one with a high clock speed. Similarly, cards as low as the 750 Ti can also run Overwatch, technically. You just won't be able to push the graphics settings up very high if you want to keep a stable FPS rate. Low and medium settings are going to be restricted more by the processor than the graphics card, while higher graphics settings become much more about the graphics card. A 3.7ghz i3 and a 750Ti will run Overwatch on low settings at 1080 resolution at a stable 60fps.
Upgrade either the processor to an 3ghz+ i5 or upgrade the graphics card to something like a 960 and you'll be able to use medium settings at 1080 with a stable 60fps. You'll need to upgrade both the processor and the graphics card to a 3ghz i5 (or better) and a 960 (or better) if you want to use high, epic, or ultra settings, or resolutions over 1080. Basically, Overwatch can run on super cheap systems, if you're willing to sacrifice visual quality. (And possibly some FPS at the very busiest times.) An i5 around the 3ghz mark and a 960 is kind of the 'sweet spot' between performance and price.