It was a win which consolidated City's place in the top half of the Premiership and leaves Palace firmly entrenched in a battle for survival.
City manager Kevin Keegan was delighted with the win but admitted his side made life difficult for itself.
They ought to have hit Palace for six or even more goals, but at the end were clinging on to a slender one-goal advantage until Shaun Wright-Phillips scored his second goal of the game and City's third in the final minute.
Keegan said: "We had our best start since we moved to the stadium, we were 2-0 up and it could have been four or five. Palace scored a goal from a set-piece and suddenly everyone became nervous, but we managed to weather the storm.
"All in all 3-1 was probably a fair result, but Palace will probably feel unlucky after their second-half showing when they asked questions of us."
Keegan again praised Wright-Phillips, believing he is destined to appear on the biggest stage.
"Shaun belongs at the very top of football, but if he leaves it another 18 months or two years before moving on he still will be only 24 or 25.
"The biggest clubs in the world will enquire about him and may have already have done so, but he is priceless to us as everything starts with him."
Palace manager Iain Dowie admitted his side paid the penalty for a dreadful start, he explained "for the first 20 minutes we didn't get going and failed to get out of the traps".
"After we scored we settled and in the second half we were on top. I don't know how we weren't given a penalty when Richard Dunne clearly shoved Darren Powell to the ground.
"Overall we didn't have enough quality and guile, though in the second half we pinned City back."
City had appeared to have the match won in the first 15 minutes by which time they were 2-0 ahead and conceivably could have been four up as their carved open the fragile Palace defence with ease.
Antoine Sibierski and Wright-Phillips both could have scored – Wright-Phillips ought to have hit the target with his shot - before City took a 12th minute lead.
Wright-Phillips ran on to a through ball from Joey Barton, turned defender Powell and drilled home an angle shot from six yards.
City quickly doubled their league when Robbie Fowler raced on to a Dunne pass, turned left-back Emmerson Boyce and fired home from six yards.
City was brimming with confidence and looked like scoring every time they went forward.
They would have built on their lead but for excellent saves from Palace's Hungarian goalkeeper Gabor Kiraly to deny Wright-Phillips, Fowler and Jon Macken.
It took Palace almost half an hour to muster their first attempt at goal when Andy Johnson burst clear only to see his goalbound shot deflected by Dunne for a corner.
Palace halved their deficit in the 32nd minute with a goal out of nothing as Powell popped up from the far post to head home a Wayne Routledge free-kick.
Kiraly also had to pull of an acrobatic save from Fowler's deflected shot late in the half as City re-imposed their authority.
After the first period provided endless thrills and spills, the second half was decidedly flat with few goals and chances being created.
Palace were unlucky not to be awarded a penalty midway through the half when television replays showed Dunne had clearly shoved Powell off the ball in the penalty area,.
City didn't seal victory until the final minute when Fowler, who had an excellent game, cut the ball back for Wright-Phillips to slot home the goal which guaranteed three points.
Man of the Match: Shaun Wright-Phillips - The diminutive winger was at his mercurial best to ensure City took all three points, netting twice to leave Kevin Keegan in raptures once again.