Boro finished the opening period three soft goals behind and down to 10 men following the dismissal of keeper Jordan Porter for a professional foul.
Things improved slightly after the interval, but the mountain Boro had to climb was far to great a task.
The result now leaves Boro with a hefty challenge on their hands if they are to force their way back into what is becoming an interesting promotion race.
The signs were not great from the very beginning, as Boro looked nervy at the back in the opening exchanges.
Jordan Connerton smashed high and wide after he had been afforded too much room in the box, then keeper Porter showed his struggles with the bright winter sunshine as he juggled a run-of-the-mill shot just past the post.
With 10 minutes on the clock, Lancaster took full advantage of a huge defensive error, when Niall Flint completely miskicked a ball into the box and Ryan Winder rolled home from close range.
Boro almost hit straight back, as Jacob Hazel popped up on the edge of the box, but his shot arrowed wide of the target.
The action quietened for a period, before Lancaster doubled their advantage thanks to more slapstick defending.
Ellis Humble tackled the ball into the path of Louis Mayers, who couldn't believe his luck as he tapped beyond Porter.
The Boro stopper showed his qualities on the half-hour as he somehow managed to hang on to Connerton's looping header.
But seconds later the Boro number one was trudging off the pitch after bringing down Connerton, who had been sent clean through on his goal.
Sub keeper Tom Morgan was brought on, replacing a clearly frustrated Craig Nelthorpe, and his first real task was to pick the ball out of the back of his net after Connerton flicked a neat header beyond his grasp.
He then made a superb save to deny City winger Jacob Gregory, who looked odds on to score from short range.
Morgan was again in the thick of the action when the second half began, once again denying Gregory, who scampered beyond a static home defence.
Lancaster hit the back of the net for the fourth time when Winder's deflected effort sailed in, but after a lengthy consultation with his linesman, referee Mr Barrott ruled it out.
An injury to Matty Bloor, who was replaced by Lewis Dennison, made things worse for Boro, before a chink of positivity emerged in the 68th minute.
Hazel was felled in the box by a clumsy Glenn Steel tackle and Adam Bolder stepped forward with his usual calm head to roll home the penalty.
Boro upped the momentum of their play in a bid to trim Lancaster's advantage further, and they could have done that as time crept further on.
Adam Bolder looped a header over City keeper Mike Hale and all Dennison had to do was nudge the ball over the line. Instead he got far too much on it and it looped up and over the bar.
Dennison almost got it right in injury time, but his sharp header was well saved by Hale.
Frustratingly for Boro, the damage had been done though, and Lancaster departed with the points, leaving the hosts licking their wounds.