Pablo Matera’s score two minutes from time set the seal on an impressive second-half performance that yielded three tries on top of Vereniki Goneva’s excellent first-half effort.
Goneva got the ball rolling with an individual effort on half-time, chipping over the Newcastle defence to score at the right corner.
And Tigers’ leading try-scorer Goneva added his second of the game and tenth of the campaign, with a smart break onto Dan Bowden’s pass in the second half.
Thomas Waldrom showed neat footwork for the third before Matera’s close-range finish secured the bonus point.
The result ensured Tigers, who had Ben Youngs, Manu Tuilagi and Toby Flood all shown yellow cards for deliberate knock-ons, picked up their fourth successive win during the Six Nations period.
Tuilagi returned from a chest injury sustained in the first meeting of the clubs in Round three in September to take his place in the starting XV.
He joined Dan Bowden in the Tigers midfield, with Goneva moving to the wing. Ed Slater, Ben Youngs and Tom Youngs returned from England duty to take their place in the side and there was a start for Matera in the back row.
The game kicked off in dry and clear conditions but the pitch was soft underfoot.
Newcastle were awarded an early kick at goal after the Tigers pack was penalised at a scrum. Lee Smith, the Falcons winger, landed the penalty from close to halfway to give the hosts a 3-0 lead after seven minutes.
It was a short-lived lead. Falcons were pinged for crossing at the restart and Owen Williams kicked Tigers level.
But the hosts were back ahead moments later. Smith made inroads down the Falcons left and was half stopped by Goneva. The ball was moved inside where Noah Cato arrived to break the Leicester midfield and score behind the posts. Phil Godman added the extras to give Newcastle a 10-3 lead.
Williams' up-and-under was well fielded by Matera to set Tigers on the attack in the Falcons half. The Argentina internatonal was well tackled by Kieran Brookes, the former Tigers prop, but the hosts went over their feet trying to secure the ball. Williams landed a simple penalty to cut Falcons' lead to 10-6 after 16 minutes.
The Tigers pack flexed their muscles with an excellent 15m drive that was dragged down on the Falcons 10m line. Ben Youngs took the penalty quickly and looked to pick out Blaine Scully on the right flank but the wing was unable to gather the long pass and the chance went away.
Tigers went close to a try moments later. Jordan Crane picked up at a ruck and made ground into the Falcons 22. He had Marcos Ayerza in support but the prop was stopped just short and his offload evaded Ben Youngs' grasp and the scrum-half could only knock on.
A solid Tigers scrum was rewarded with a penalty on the Newcastle 10m line but Williams was wide with his kick into the wind as Leicester trailed 10-6 after 30 minutes.
Tigers were on top at this stage and tested the hosts’ defence through Goneva and then Dan Bowden. Bowden was held in the tackle and Williams landed a simple penalty to leave Tigers 10-9 behind seven minutes before the break.
It set up a frantic finish to the half. First Logovi’i Mulipola was penalised for a push on Smith and Godman restored Falcons’ four-point advantage with the resulting penalty.
Tigers’ response was immediate. Bowden’s delayed pass found Goneva in space on the right touchline where he broke through Smith's tackle and held off Adam Powell before chipping over Alex Tait into the right corner where he won the race to the ball for his ninth try of the campaign.
It put Tigers into the lead for the first time in the game and they went in 14-13 ahead at the break.
Tigers made the ideal start to the second period when Williams, with the wind at his back, landed a penalty from the 10m line to extend Leicester’s lead to 17-13.
The Tigers pack won another penalty at a scrum on halfway and Williams landed his second kick in the space of five minutes at the start of the second period to put Tigers 20-13 ahead.
Tigers were called on to defend their 22 as Newcastle probed for an opening. A good tackle by Matera allowed Goneva to steal possession at a ruck and Williams cleared deep into the Falcons half.
Back Falcons came with Cato stepping off the right wing to create an opening for the offload. However, Ben Youngs knocked on as he tried to intercept and was shown a yellow card by referee Greg Garner.
Falcons opted for the corner and had Tigers under pressure with the drive. Mike Blair sniped down the side and was stopped by Matera but Scott Lawson emerged with the ball and dived over at the left corner for the second Falcons try. Smith pulled the conversion across the posts as Tigers led 20-18 with 21 minutes left.
A barrelling run by Tuilagi gave Tigers great field position on the left. And they thought they had scored a second try when neat hands by Bowden and Matera put Scully over at the corner. However, referee Garner ruled Matera’s final pass went forward and disallowed the effort
Falcons were unable to clear their 22 from the scrum, however, and Tigers had them under pressure at the lineout. Crane collected the ball to set up the drive and, with the advantage of a penalty, Bowden, operating at scrum-half in the absence of Ben Youngs, fed Goneva 10m out. The wing broke the tackles of Cato and Blair to cross for his second of the game. Williams added the extras to extended Leicester’s lead to 27-18.
Goneva was close to his hat-trick moments later when he read Gonzalo Tiesi’s pass in the Falcons 22 but he was unable to hold onto the ball with the line in sight.
David Mele replaced Ben Youngs at the end of the scrum-half's sin bin period.
Tigers did cross for their third with 12 minutes to go. Thomas Waldrom, on for Gibson, collected Mele’s neat offload and showed nice footwork to break the tackle and score behind the posts. Williams added the extras as Tigers led 34-18.
Tigers went down to 14 men on 70 minutes when Tuilagi was shown a yellow card for a deliberate knock-on as he attempted to intercept a pass on the Leicester 10m line.
Tigers had one last chance to secure the bonus point with a 5m lineout two minutes from time. Tom Youngs peeled off the back of the drive and fed Mele who was stopped just short. But Matera followed up and forced his way over for his second try in Tigers’ colours.
It secured the bonus point victory and, converted by Flood, set the seal on a 41-18 win.
Tigers finished the game with 13 men when Flood became the third player to see yellow for a deliberate knock-on.
The visitors withstood one last attack, holding up the Falcons over the line to bring the game to an end.