To pry (or pry out) information from someone is another common way of saying it. (I'm surprised no one else has said this yet.)
to pry (verb) 2. trans. To obtain or extract, esp. with difficulty. Usually with out (of). (OED)
I think the Ngrams below make a strong case for pry coming in 2nd behind elicit. See 2 Ngrams below.
1896 C. M. Sheldon His Brother's Keeper iii. 66 We managed to pry out of him that he had seen you and Eric go down the ladders.
1900 G. Ade More Fables 46 Usually, when she wanted any Pin Money, she had to Pry it out of him.
1938 N.Y. Times 23 Sept. 37/2 He had pried it out of Fielding Yost in four hours of pointed questioning and evasive answering.
1976 Time 20 Dec. 1/2 When Watergate raised questions about the integrity of the Executive Branch, Congress appointed an independent prosecutor to pry out all the facts.
2004 M. Flook Lux 128 Alden followed the scanty directions she had pried out of the minimart clerk.