Eastman’s equaliser after 83 minutes cancelled out man-of-the-match Shaun MacDonald’s opener and brings Colchester’s tally to nine draws from their last 11 league outings.
The travelling U’s supporters were preparing to celebrate their side opening the scoring after 10 minutes when Andy Bond’s strike crashed against goalkeeper Darryl Flahavan’s crossbar, only for the Cherries to scramble away the loose ball.
Just a minute later Paul Groves’ side went up the other end to take the lead in controversial circumstances when a deft chip over the Colchester defence by Scott Malone into Wes Thomas, who appeared offside, was despatched after the Cherries striker had rounded goalkeeper Mark Cousins.
Bournemouth could have secured the points in the 53rd minute when Cousins fumbled Marc Pugh’s corner, which dropped kindly for Malone, who struck the follow-up against the post.
But the Cherries were made to pay for their spurned chances in the 83rd minute when Eastman reacted quickest in a congested penalty area to side-foot substitute Michael Rose’s delivery beyond Flahavan.