Arsenal ratings: Ramsdale 10/10 in flawless performance
Gabriel flicked a header home from Bukayo Saka's corner on five minutes. Arsenal continued to completely dominate the hosts, who beat Manchester United in their last home league match, and soon enough Smith Rowe latched onto the loose ball to make it two.
Leicester grew into the match and had several chances to get themselves back into the contest before half time, only to find Ramsdale in inspired form.
Ramsdale's leap to keep James Maddison's free kick out just before half time was a contender for save of the season, clawing the ball away as it seemed destined for the top corner in spectacular fashion.
After the break, Leicester continued to create chances which on another day they would have converted, but Ramsdale refused to be beaten, bailing his side out time and again to ensure a vital victory on Arsenal's road to recovery.
Leicester full-back Luke Thomas drilled wide early in the second half as Leicester continued to press, before another brilliant Ramsdale save denied Ademola Lookman.
Ramsdale was then at it again to smother at the feet of Harvey Barnes.
Of the goalkeepers to have faced more than two shots on target this season, only Edouard Mendy (89.7%) is enjoying a higher save percentage than Ramsdale (85.7%), who has saved 24 of the 28 shots on target he has faced.
Arsenal have been steadily improving under coach Mikel Arteta after a difficult start to the season, following on from last term's eighth-placed finish.
"It is a superb result away from home against a top team," Ramsdale told BT Sport. "We started really well and got two good goals.
"Thankfully it was one of those afternoons that I contributed. We should have had a few more clean sheets [this season] but I'm happy with this one."
A seventh win in that unbeaten run of nine means Arsenal climb to fifth in the standings, above Leicester who drop to 10th, with the rest of the Premier League teams still to play this weekend.