McCall's men looked to be heading for defeat in another must-win game when the17-year-old fired Peter Jackson's Imps in front, but they couldn't hold out against a Bradford side desperate for a win.
Hutchinson took his second half chance following a shocking error by Bradford skipper Graeme Lee and Jackson will have been impressed by the way the teenager kept his head to fired through keeper Rhys Evans' legs from 16 yards.
The Bantams dominated the early exchanges an Imps' keeper Robert Burch did well to block a couple of breaks by striker Michael Boulding.
The former Mansfield striker eventually got the ball in the net at the end of the half, but his goal was ruled out by an offside flag.
Lincoln's own hopes of forcing their way into the play-offs were boosted when Hutchinson's a cool finish put them ahead after 47 minutes.
The youngster took full advantage when Lee lost possession and hesitated 30 yards out, giving Hutchinson a clear run on goal.
The teenager drilled the ball between Evans' legs and with Bradford's play-off hopes hanging by a thread McCall was forced to make a change.
Winger Steve Jones was pushed up front alongside Peter Thorne and Paul Mullin and the switch almost paid dividends on the hour mark.
Jones' flick on fell into Thorne's path, but from close range the striker's instinctive shot hit the bar.
The Bantams levelled five minutes later when Thorne's lay-off was met by a low shot from Bullock, but with a draw no good for either sides' promotion hopes, it was Bradford who finished strongly.
Jones saw his shot deflected wide of goal by Paul Green and two minutes from the end Thorne latched onto Mullin's header only to see his shot comfortably covered by Burch.
In the closing stages Lincoln substitute Ben Wright headed over, but Bradford had to settle for a point and now face an anxious run-in with only three games to go.