The #1 thing* that will get you to a phone screen is keywords that match what the hiring manager (and usually the screening software) is looking for. Those keywords are usually a combination of technologies, skills, responsibilities, and companies. Yes, where you worked previously is important, and yes that makes it a vicious cycle for a lot of people.
The #2 thing that most hiring managers look for is directly relevant experience matching the responsibilities of the role in question. Yes, that sucks because it means if you haven't yet gotten to the level of doing the work in the new role then you're at a disadvantage. The way around this is to ask for responsibilities at your current job that you want to do at your next job.
The advice in this article tends to come into play after those two factors are met.
*excluding an internal referral.