Any deduction that reduces your taxable income may reduce your tax bracket; that includes not only the standard deduction or schedule A itemized deductions, but certain other less common deductions.
However, your entire income is never taxed at the highest bracket. Suppose you are married filing jointly and your gross taxable income is $110,000. After the $25,100 standard deduction, your taxable income would be $84,900. However, this is not taxed at 22%. Instead, the first $19,900 is taxed at 10%, the next $61,150 is taxed at 12%, and only the amount over $81,050 ($3850 in my example) is taxed at 22%.
In other words, you are never in a situation where a small raise that puts you in a higher bracket subjects all your income to the higher rate, just the amount that is over that threshold.
Then of course, your tax will be reduced by any allowable credits, such as for dependents and certain other activities.
