I read all the +3 -> +5 comments here and am shocked to see no one mention the importance of referrals!
You already know people connected to the industry -- talk to them! Ask your profs if they know anybody in the industry. Ask your jobful friends to pass your resume along. Is there a famous prof at your uni? Did you take a class with them? Bring your chutzpah to their office and ask for a rec.
A referral from a trusted third party is thousands of times more likely to get your foot in the door than your resume, no matter how bloody sparkly the thing is.
Case in point, I graduated summa cum laude from an Ivy school, and no one really gave much of a shit. Until I knocked on my algo prof's door once during his office hours, asked him whether he knew someone in industry looking for a smart hard-working youngster. He gave me the name of his contact (the CEO of a tiny co). (I didn't even do that well in the Prof's class, slightly below median IIRC.)
Next thing I know the CEO's shaking my hand congratulating me on my new 50%-pay job. He's telling me "boy have you ever got a lot to learn, but Prof so-n-so says you're smart and you do seem to come off that way". Worked my arse off til it turned into a real job. And now there are *2* people out there who think I'm smart, so, you know, twice the network :)
If you don't have a network, make one. Think about doing an unpaid internship at a company that has a future. (Look into funding options from your uni for this kind of stuff.) Be careful with this one -- the network you create here must be valuable to justify the work and the resume gap.
I had the privilege once to speak with the former-CFO of Coke, and asked her (rather lamely) how one winds up being the CFO of Coke. She said, "If you really want a big-time job you gotta be aggressive and you gotta be charming."
Note that "qualified" is not a part of that sentence.
Broken thinking. Getting hired isn't about being good at the job. It's about being good at getting hired, which is a largely orthogonal skill set.
Need new skill set = need to practice. Interviews are like first dates: they pretty much all suck, but get less nerve-wrecking with practice.
I should mention that once you have job 1, the network it creates (or doesn't create) will bear heavily on how your search for job 2 goes. So take good care of your network at job 1. I've seen a ton of smart people with amazing resumes, who are actually quite good programmers, who can't find jobs because they are huge pains in the ass. The days of the cranky-bitch-genius-programmer are limited (if not completely over), because there are plenty of pleasant-genius-programmers out there who need jobs too.
Approach your job like a pro: learn the politics and the people, be friendly, be polite but not stodgy. Choose very carefully which personal details to share with which people. Never express a negative emotion unless you've thought about it extremely thoroughly. Never write an email to/from a work account that you wouldn't want the CEO to read. Get people to like you: morally it shouldn't matter, but practically it makes a gigantic difference to how your career will go.
Finally and of course most importantly, work your ass off and get results. Nothing will make boss-man like you more than if you are generating two times the output as everyone else, with a smile and a joke handy at lunch time. It makes him look fabulous to his boss, and ten years from now when he's working at google (or whatever the "google" of 2020 will be, probably "google"), guess where you can ship an email and probably get a job.