Their recent habit of coming slowly out of the blocks continued.
They had conceded goals in the opening minutes of their previous two home games and ended up empty handed each time and found themselves trailing again after just seven minutes.
But they produced a stirring comeback to overhaul playoff chasing Lincoln and will give new boss Stuart Watkiss plenty of hope for the relegation battle ahead.
New signing Billy Jones was slow to find his bearings on his debut and Lincoln were quick to punish him.
Craig Westcarr took advantage of the left back's slow reactions to gain possession and sweep the ball over for Francis Green to drive the visitors into the lead from close range.
Harriers already had a warning when Westcarr headed against their crosbarr in the fourth minute.
But they gradually sorted themselves out in defence and deservedly equalised in the 16th minute.
Shortly after Gary Birch saw a goal disallowed for offside, Harriers won a corner and Sturrock forced the ball home from six yards from Jones' cross.
It was the striker's third goal in five games since signing from Plymoth.
Two minutes into the second half, only a desperate save from John Danby kept the home side in front.
Jamie McCombe looked set to score as he hooked a volley goalwards from 18 yards, but somehow Danby dropped to his right and flicked the ball away for a corner.
Four minutes later Harriers were ahead thanks to a brilliantly-worked goal from Russell who played a clever one-two with Dean Keates before coolly slotting home past keeper Alan Marriott from eight yards.
Substitute Chris Beardsley brought a fine stop from Marriott as the home side continued to dominate, but they had to survive some anxious moments in the closing minutes.
McCombe looked certain to score but Danby saved with his legs, and then Gary Taylor-Fletcher chipped a dipping cross onto the bar with four minutes remaining.