After a third minute Tom Elliott had given the U's an early advantage, City rallied and were rewarded when Andrew Boyce headed home following an Adam Smith corner shortly before the break.
The second period was all City, although the old adage that you've got to turn possession into goals came to the fore as, with nine minutes remaining Harrison Dunk got the better of the otherwise impressive Dan Gray to set up substitute Adriano Moke for a unjustified winner.
City boss David Holdsworth named an unchanged 16 to the one that was on show against Kidderminster Harriers on the opening day of the season for this Tuesday night clash against Cambridge United at the R Costings Abbey Stadium.
Looking resplendent in the new all-white away kit, the Imps were up against a Cambridge side who went into the game on the back of a 1-1 draw at Forest Green Rovers at the weekend. The hosts kicked off.
Cambridge were quick to put the Imps on the back foot and after Paul Farman had claimed an early Andy Pugh cross, he was left helpless just three minutes in as when Robbie Willmott whipped in a centre from the right, in nipped Tom Elliott to plant a firm header past the City stopper to give his side an early lead.
City looked for a quick response with a long Dan Gray throw-in hitting a home defender with appeals for hand-ball being waved away by referee Rob Whitton. A couple of minutes later home stopper Jonathan Hedge fell heavily as he claimed an Imps' free-kick but was okay to continue.
Good work from Gray saw him win a corner in the 11th minute as the Imps stepped things up in search of an equaliser but referee Whitton spotted a foul on Hedge as Smith's floated delivery went into the six-yard box.
Duffy had a header saved by Hedge seven minutes later after a John Nutter free-kick was nodded across the area by Andrew Boyce at the back post. Luke Daley, at full stretch, then headed wide as the Imps kept probing to get back on level terms.
At the other end Tom Shaw fired well wide after a stray Gary Mills header gave the United midfielder a sight of goal before the advancing Harrison Dunk headed well over from a Willmott cross.
Dunk won the hosts' first corner shortly before the half-hour mark but Elliott's stooping header flew well off target and as City responded Smith drew a foul from his man to earn the Imps a free-kick which was hurriedly hacked away by the home defence.
City kept probing away but found that killer final ball elusive as the half wore on, but when a neat Smith chip forced Jennings to head behind under pressure from Daley, it gave the winger the chance to float in a 39th minute corner which had Hedge in all sorts of problems. And, with the home 'keeper caught flapping at fresh air, up rose Andrew Boyce to head home his first City goal from six yards.
With the home fans silenced, City continued to enjoy the better of possession in the run up to three additional minutes and midway through this added time a City corner ended up seeing John Nutter fire over after Smith's ball to Taylor was laid into the left-back's path.
HT: Cambridge 1 Imps 1
Whilst City emerged unchanged, ex-Imp Sam Smith was brought on prior to the start of the second half for goalscorer Tom Elliott.
The Imps were the first to press with both Power and Gray having efforts charged down after a long-throw from the latter caused problems for the United defence and with the ball remaining in the home half a Power cross just evaded Duffy at the back post.
Two City corners saw them keep up the pressure and when the latter was headed goalwards and palmed away by Hedge, Smith saw his follow-up effort cleared off the line with Hedge beaten. Another Imps' flag-kick was then played into the mix before Power was pulled up for a foul.
A dipping Power centre was then headed behind with Hedge punching the corner clear as the Imps continued to push the hosts on the back foot, playing some excellent football in the process.
In the 59th minute a second United change up front saw Adriano Moke come on for Andy Pugh and he was quickly in the action, forcing Farman to make two saves in quick succession following a rare Cambridge attack.
A great forward ball from defence by Gray saw Taylor come within inches of connecting as Hedge sprinted off his line whilst shortly afterwards another Gray ball was flicked on to Taylor who was flagged offside. He was duly cautioned, for the second game running, for kicking the ball goalwards.
In the 72nd minute a Cambridge corner was cleared by Smith and when the ball was pumped forward again Mills was left clutching his head following an aerial challenge midway inside the City half.
Despite dominating for the majority of the second period, the Imps were undone nine minutes from time when, after Dunk got the better of Gray for the first time in the game, he squared for substitute Moke who took a touch before blasting past Farman and into the roof of the net from 10 yards.
With the goal knocking the stuffing out of the Imps following their impressive showing after the break, a double change for the Imps saw Vadaine Oliver and Jake Sheridan come on for Luke Daley and Adam Smith.
Cambridge were now keeping the ball in the City half with a corner being cleared by Gray but from the resultant counter-attack, Taylor's attempted cross to Sheridan landed straight in Hedge's gloves.
City had four added minutes in which to salvage something from the game and in a last change, Nicky Nicolau came on for John Nutter. Blaine Hudson replaced Harrison Dunk for the home side at the same time as the seconds ticked away, ultimately towards a defeat for the hardworking Imps.
FT: Cambridge 2 Imps 1
City: Paul Farman, Dan Gray, Andrew Boyce, Tom Miller, John Nutter (Nicky Nicolau 90+4), Gary Mills, Alan Power, Adam Smith (Jake Sheridan 84), Luke Daley (Vadaine Oliver 84), Rob Duffy, Jamie Taylor.
subs not used: Graham Hutchison, Jake Turner.
goal: Boyce (39)
booking: Taylor (66)
Cambridge: Jonathan Hedge, James Jennings Josh Coulson, Tom Shaw, Tom Elliott (Sam Smith 46), Harrison Dunk (Blaine Hudson 90+4), Rory McAuley, Scott Garner, Andy Pugh (Adriano Moke 59), Rossi Jarvis, Robbie Willmott.
subs not used: Ricky Wellard, Adam Marriott.
goals: Elliott (3), Moke (81)
Referee: Rob Whitton
Assistants: Jonathan Pickford & Neil West
Fourth Official: Stuart Pawley
Attendance: 2,456 (278 City supporters)