The deadlock was broken on the hour by Jamaican striker Shaw, before Lioness' Kelly rounded off the scoring on a day which Leicester fans will still believe was a sign of improvement as they battle for Barclays Women's Super League survival.
There were four changes to the side that were defeated on penalties by Reading last weekend, with new signings Georgia Eaton-Collins and Courtney Nevin making their first starts, replacing Molly Pike and Jemma Purfield, who dropped to the bench.
Despite facing top-level opponents, it was the Foxes who started brightly and forced the first opening of the game. After winning back possession towards the visitors' corner flag, a well-placed cross into the box was sent towards goal by Hannah Cain, but Ellie Roebuck was there to make the stop.
After this, the Citizens took a bit more control, calling Janina Leitzig into action on several occasions, most potently when in-form striker Shaw broke through and looked certain to break the deadlock, before the German 'keeper got down to turn it behind.
Leicester were having great fortune with Bott overlapping on the right wing, however, this did leave space at the back for Lauren Hemp to utilise when Man City turned over possession.
Heading into half-time, it was the visitors who looked in control, forcing Leitzig to stay alert, as the scores remained goalless at the interval.
Into the second half and the task was the same - to defend Man City's advances. Hemp continued to provide a spark for the away side, and through her efforts, they were able to open up some chances.
Leicester's new shot-stopper was having a wonderful game, but the deadlock was finally broken by Shaw, when a cross into the box connected with the Jamaican's head, before looping into the net.
With it all to do, it's fair to say that the Foxes lost some of their attacking prowess that they were showing in the first half, and manager Willie Kirk was keen to make changes accordingly.
Ava Baker and the returning Josie Green were introduced, with the latter making her first appearance since her calf injury.
Not long after, a second goal was scored on Filbert Way, as the travelling Manchester side strengthened their lead. Kelly, picking up the ball on the right wing, drove forward, cut inside and let loose an impressive left-footed effort which flew past Leitzig into the net.
With this two-goal lead, the visitors saw fit to replace the goalscorers, and this allowed Leicester to push higher up the field and look to create chances of their own.
Their best moment came minutes from time when Cain broke through and had an effort on target, but Roebuck made the stop to prevent any chance of a consolation goal, and seconds later the referee brought an end to proceedings, confirming a home defeat for the Foxes.
Major moment - Shaw's opener
Hanging on for well over an hour, it was bitterly frustrating to see the ball rustle the net, but when playing against one of the best teams in the league, with one of the best striker's in the world, a goalless game was a long shot.
Who impressed? - Janina Leitzig
It was a spirited performance from all involved, but Janina Leitzig's display in the Leicester net was remarkable. Countless efforts saved, it will come as comfort to the Foxes' fanbase as they will need a few clean sheets to help retain their WSL status.
Where do we stand - 12 in the WSL
The loss leaves City at the foot of the standings, with three points.
Coming up - Liverpool (A)
WSL action continues for the Foxes as they travel to Merseyside to take on Liverpool on Sunday 12 February (2pm GMT kick-off) at Prenton Park.
The details…
City: Leitzig; Bott, Howard (Green 71'), Plumptre, Nevin (Purfield 80'); Eaton-Collins (Smith 84'), Tierney (Simon 90'), Whelan (c); Goodwin (Baker 71'), Cain, C. Jones (Pike 80')
Subs: Lambourne, Levell