City totally dominated the first half but failed to take their chances and went in at the break a goal down.
Dale then defended well and should have put the result beyond doubt, before Hone stole in at the far post and smashed the ball into the back of the net four minutes from time.
Dale were forced to defend right from the start with Rory McArdle lucky to escape with a yellow card after a dreadful challenge on Scott Kerr after just 52 seconds.
Lincoln kept up the pressure and Lee Frecklington was denied by an excellent diving save from Sam Russell.
Russell saved again the 12th minute from Lee Beevers, but was lucky five minutes later when he fumbled a shot from Dany N'Guessan but somehow managed to push the ball over the bar.
Kerr's corner picked out Lenell John-Lewis, but from six yards out the striker headed over.
Rochdale sneaked in front in the 26th minute with a superb goal. A half clearance from Hone fell to Adam Rundle, who lashed the ball into the net from 25 yards with a first-time left-foot shot.
Lincoln continued to create chance with Russell saving from Hone and N'Guessan.
Six minutes before the break N'Guessan broke into the box and appeared to have his legs taken from him by Marcus Holness, but referee Chris Sarginson rejected appeals for a penalty.
Lincoln's frustration began to show in the second half with manager Peter Jackson sent to the stands for an outburst at Mr Sarginson.
Rochdale created a great chance in the 76th minute when Chris Dagnall put Gary Jones clear, but the skipper failed to find the target from a good position.
Even after Hone's equaliser Rochdale had the chance to win the game. The ball fell kindly to sub Adam Le Fondre, but from six yards out he sent a weak shot straight at home keeper Rob Burch.