Because we also have solar panels, and we changed rate plans, buying an EV did make our electric bill go from paying about $1,000 a year to getting a check from SoCalEd for $74.26 for the first full billing year with the EV.
Our Spark EV has never been charged anywhere except at home since we bought it in January 2014. On the other hand it only has 5,370 miles on it after 25 months, so I don't do much driving.
Our PV solar power setup is large because we use a lot of power for koi pond pumps. Since it was designed and installed in May 2012 we have also optimized energy use where feasible. When we got the BEV we switched to a Time Of Use rate plan for EV owners, previously we were simply tiered.
For our net metering billing year from June 2014 to June 2015 we were net energy producers, thus the check.
So the solar panels are primarily involved, but the switch to a TOU rate plan for EV owners was also a factor. One might say getting an EV helped lower our electric bill, but few people only drive 2500 miles a year, so it's definitely a corner case.
For those charging an EV at home, look into your utility's TOU rate plan offerings. It might save you a lot of money.