Afterwards, Leicester manager Craig Levein said: "We spoke to Keith earlier in the week about not scoring enough goals. But he got in some good positions and although the ball fell kindly for him, it was a very well executed shot."
Levein admitted that his side had underperformed, but was pleased to see City extend their unbeaten run to seven.
He said: "We took a little step back today, but what is encouraging is we got a point where if previously we had underperformed, we would have lost. My one criticism is that we didn't create enough chances in a home game as we should have. But we didn't play particularly well, and I know that we can perform much better."
Crewe took the lead on 35 minutes when they launched a counterattack through Lee Bell and Anthony Tonkin which ended with White holding off Matt Heath to drill home from 15 yards.
After the break, Ian Walker prevented City from falling further behind when he blocked Luke Varney's 15-yard shot.
And City were level on 58 minutes when substitute Mark De Vries failed to get a clean connection on Jordan Stewart's cross with a loose ball falling to Gillespie who swept home from eight yards.
On 73 minutes, Danny Tiatto cleared a Chris McCready header off the line, and in time added on Johannes Gudjonsson had a chance to clinch it for City, but his long-range drive flew narrowly over.
Afterwards Crewe manger Dario Gradi said: "Luke Varney could have put us two up, but the keeper did well to stop his shot.
"But I am not going to criticise him because he is a good player who is going to score plenty of goals.
"We are now learning how to cope without Dean Ashton. Luke and Andy White were outstanding and their centre-halves will have known they've been in a game."