To put it bluntly, it is as wrong and deceitful to conceal information as it is to give dishonest details. Leave aside the fact that you are cheating the employer and yourself, it could have far-reaching issues that may jeopardize your future job prospects and career. You need to read the finer print that is mentioned in the terms and conditions of any job application. You may see the text that if you provide incorrect or wrong information, you are liable to "face dismissal and termination of your candidature/ service/contract and are also liable to face other penal action as per the law". This is the exact text I have seen often when submitting jobs here at our site. Also, keep in mind that your dishonesty could cause some eligible candidates to lose out on their candidature.
That said, note, however, that in some job recruitment notifications, it is mentioned that candidates with higher qualifications will be given preference. What I suggest is that you be honest. Since you indicate that you have already applied for the post if you are required to appear for an entrance test and/or interview you should inform them that you are a Graduate and had omitted to indicate it in your application. Be truthful and state that you were hoping to get the job. Do not take up the job with the concealed information. No matter that you do not get selected at all, You will not have to face the future ignominy of being dismissed from the job and having a black mark against your name, something that would be harmful in the future as you will then not get good references. More important, at least your conscience will be clear.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell