Wes Morgan and Jamie Vardy scored in either half as Leicester beat Bournemouth 1-0 at the King Power Stadium.
The Foxes captain, whose stoppage time winner beat Burnley last time out, scored for a second straight game for the first time after turning Ben Chilwell's shot past the despairing Asmir Begovic (11).
Bournemouth offered little in response, with Callum Wilson having the best chance to level but Kasper Schmeichel was equal to it.
And with eight minutes left Vardy secured the win by doubling the lead, flicking Youri Tielemans' right-wing cross into the net (82).
The result lifts Leicester into eighth in the table, while Eddie Howe's side remain in 12th and 10 points above the relegation zone.
It was another poignant afternoon at the King Power, with the game used to remember former chairman Vichai Srivaddhanaprabha, whose 61st birthday it would have been this coming week.
Arguably it was therefore fitting that two players who underpinned the 2015-16 title success under his stewardship proved the difference as Leicester stayed in the race for a European place.
Having come off the bench to score the winner against Burnley last time out, Morgan was installed from the start in the absence of the suspended Harry Maguire.
And once again the Jamaican defender's impact was felt in the final third as he gave Leicester an early lead.
James Maddison caught out the Bournemouth defence by floating a corner out towards Chilwell and the full-back's cross-shot fell the way of Morgan who instinctively flicked the ball beyond the returning Begovic.
Bournemouth did belatedly burst into life and should have drawn level when Ryan Fraser crossed for Wilson, but Schmeichel's reflexes were equal to his close-range effort.
Vardy passed up a glorious chance to double the hosts' lead after being found free in the area by Ricardo Pereira, but shot wastefully wide.
But such profligate finishing was offset by rare Cherries attacks, with Ryan Fraser's weak effort and Josh King's mistimed half-volley the best they could muster during the remainder of the first half.
If Bournemouth's forays into their opponents' final third were rare in the opening 45 minutes, after the break they became even less common as Leicester snuffed out any threat.
Diego Rico, Dominic Solanke and Junior Stanislas were all introduced in the second period but none of the trio made an impression on an easy afternoon for the home side.
It was therefore little surprise when their 10th away defeat in 11 Premier League games was confirmed as Vardy was given one chance too many, clattering a header in off the crossbar after being found by a delightful Tielemans centre to give Rodgers a third straight win.
Opta stats
- Leicester have won three consecutive Premier League games for the first time since a run of four ending in December 2017.
- Bournemouth are winless in six away league visits to Leicester (W0 D3 L3), since a 1-0 win on Boxing Day in 1988 under Harry Redknapp.
- Leicester manager Brendan Rodgers has won all four of his games in all competitions against Bournemouth - the only teams he has a better 100% win record against in his career are Hamilton Academical (9 wins), Fulham (7) and Coventry City (5).
- Bournemouth boss Eddie Howe is winless in eight away league visits to Leicester City during his managerial career (W0 D4 L4).
- Bournemouth have lost 10 of their last 11 away Premier League games, winning the other.
- Jamie Vardy has scored five goals in his last five Premier League appearances, after netting in just one of his previous six.
- Leicester's Ben Chilwell has provided three assists in the Premier League this season, more than he registered in his previous two campaigns for the Foxes (2).
- Leicester's Wes Morgan has scored in consecutive Premier League appearances for the first time in his career, also netting three goals in his last four.
Man of the match - Wes Morgan
Once again key in the final third, it was Morgan's influence in the defensive third which set him apart from the rest during a comfortable win at a sun-decked King Power.
Callum Wilson and Josh King are among the most elusive strikers in the top flight but they were kept quiet for long periods by the captain, who covered ably for the absent Maguire.
The managers
Brendan Rodgers: "The reason I came is that they're a fantastic group of players. It is going to take time to holistically get over our ideas so it becomes the norm for the players.
"What they have shown is a wonderful appetite to learn and embrace how we want them to play. Like I say they have shown really good tactical ideas in the games and that is very pleasing.
"I think we've seen that today, the hunger in the players and how focused they were on the game. We had a lot of chances and opportunities but we took the most important ones and kept a clean sheet which is equally important."
Eddie Howe: "We didn't play anywhere near the levels that we're capable of doing. We'll have to analyse and reflect on what we did today.
"Goals change games, I think that is a well-used cliché. Their early goal put us on the back-foot. There was an opportunity for us to equalise, we didn't take it but we had a long time in the game to force our way back.
"It was one of those days we tried a lot of different things in the game to try and spark an upturn in our performance but it didn't happen."
What's next?
Bournemouth host Burnley while Leicester go to Huddersfield.