It was not without the kind of faults that have become the norm of late but Pep Guardiola finally rebooted his winning Manchester City machine in his 500th match in charge. A relieved Guardiola blew kisses to the travelling supporters at the final whistle, and conducted their choruses, but there were several indicators that the contraption he has crafted is damaged goods, not quite what it once was. With 70 minutes on the clock and City a goal in front courtesy of Savinho’s first-half strike, Stefan Ortega was booked for time-wasting and the reality is they made hard work of beating the third-worst team in the division.

“Champions again, olé olé,” came the chant from the away end but time will tell. It feels fanciful at this stage. City are fifth, four points off fourth-placed Chelsea, who visit Ipswich on Monday. At the same time, perhaps the end of a dire run will prevent a dreadful season?

Erling Haaland sealed victory, heading in to cap a slick move, kickstarted by the substitute James McAtee. City flicked through gears they have struggled to find in recent weeks, shifting the ball from right to left and Haaland, played onside by Conor Coady, powered in unmarked after meeting Savinho’s cross.

Related: Relief for Pep Guardiola as Manchester City stop rot with win at Leicester

Savinho got City up and running, feasting on the rebound of a bouncing Phil Foden shot, parried by the Leicester goalkeeper, Jakub Stolarczyk, but City’s second win in 14 matches, and second clean sheet in that run, was anything but routine. It was a performance that underlined Guardiola’s wishes to strengthen in January but maybe a wacky contest was inevitable given this was a meeting of two of the division’s most out-of-form teams. Leicester, while promising going forward, are also one of the most charitable sides. Still, a year that began in such style, culminating in a fourth straight Premier League title and a 32-game unbeaten run, ended in familiar fashion.

City led from the 21st minute but there was no comfort blanket until Haaland’s header after 74. Jamie Vardy’s presence proved unsettling, the striker, who turns 38 in a fortnight, returning to the starting lineup to lead Leicester’s attack and keep Nathan Aké on his toes. Vardy punched the visitors’ crossbar and ended up tangled in the goal net after lifting a shot over from Stephy Mavididi’s sumptuous cross. Vardy slithered between Aké, who was replaced by Kyle Walker midway through the second half, and Manuel Akanji but could not get his effort on target. Vardy was the catalyst for the move that prompted Akanji to prevent James Justin from hooking the ball in minutes earlier. At 2-0 down it was Vardy who rattled a right angle of Ortega’s crossbar with a looping header.

Bilal El Khannouss’s feathery, arcing cross from the right flank soon after the half-hour was the perfect example of quite how close Leicester came to an equaliser on several occasions. El Khannouss’s inviting ball eluded Justin, Vardy, who appeared to intentionally leave it, and Facundo Buonanotte, who was left butting his forehead against the back post in frustration. Buonanotte grew familiar with the woodwork, eight minutes later sending a header against the same post after Josko Gvardiol and Savinho failed to clear the remnants of El Khannouss’s cross from the left.

City offered Leicester encouragement, windows of opportunity. City’s first scare was averted when Vardy, after racing on to Buonanotte’s through ball in the left channel, was flagged offside after being felled in the box by Ortega, who looked sheepish before looking to his left for confirmation from the assistant referee. Then Gvardiol undercooked a header back to his goalkeeper, allowing Vardy to nip in and trouble Ortega, who dashed towards his near post to make the save.

It was plain City were without the aura that has been absent for a while now. Kevin De Bruyne, Guardiola’s sole change from their draw against Everton, shanked a routine clearance at the front post after an El Khannouss corner.

For City, a welcome buffer would have arrived 10 minutes before half-time had Haaland, after surging past Jannik Vestergaard and sidestepping Boubakary Soumaré, sent his shot the other side of a post after City zoomed forward after Mateo Kovacic pickpocketed El Khannouss on halfway. De Bruyne wellied an early shot over but Haaland had City’s first notable chance, Stolarczyk repelling his first-time shot, from De Bruyne’s cutback, with his left boot.

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Stolarczyk, who kept his place in goal, should have done better with Foden’s awkward effort but had no chance with City’s second. McAtee eliminated Victor Kristiansen with a jink and from there City clicked. De Bruyne took over the baton, moving the ball to Savinho who supplied the cross. Haaland, who had a single touch in the opposition box against Aston Villa eight days ago and scored three times in the league since September, made Leicester pay. As Haaland, who became a father in recent days, said afterwards: “Shit happens.”