Jonny Wilkinson came through his first 80 minutes of the season in a scrappy game but the real talking point came early in the second half after a James Hamilton try had put the home side 11-9 in front.
Andy Goode struck the conversion and, although television replays showed the kick had drifted just the wrong side of the posts, the touch judges nevertheless raised their flags.
After Goode added a penalty to stretch his side’s lead to 16-9, the Falcons levelled with Robbie Morris’ late converted try but Newcastle director of rugby Rob Andrew will have headed north feeling he was short-changed.
Leicester’s Julian White and Newcastle’s Andy Perry were both sent off for fighting in first-half added time but the Tigers know they must improve when they face Clermont Auvergne in the Heineken Cup next week.
Wilkinson, returning after an appendix operation, did not take long to make his first impression.
His fourth-minute penalty from 45 metres bounced off the post but the Falcons regained possession and he slotted a right-footed drop goal from just inside the 22.
With Martin Corry making his presence felt in the lineout, the Tigers’ first real spell of pressure saw the hosts draw level thanks to Goode’s well-struck penalty from around 45 metres.
Another kick from Goode just in front of the posts took Leicester ahead but Wilkinson pegged them back from a similar distance following a charge up the middle by centre Mark Mayerhofler.
That proved the end of Graham Rowntree’s evening as the veteran prop limped off 30 minutes into his 200th league start for the Tigers.
Wilkinson had already almost had a kick charged down by Harry Ellis and required almost five minutes of treatment on his left leg when the Tigers’ scrum-half caught him late in the 40th minute, an offence that resulted in Matt Burke moving the Falcons three points ahead.
Seven minutes into added time Goode needlessly caught Wilkinson high and late, earning himself a yellow card before Falcons’ hooker Andy Long suffered a similar fate a minute later for illegal play at the breakdown.
White and Perry were each shown the red card by referee Tony Spreadbury for fighting on the floor after Ellis had broken away to take first-half added time up to 14 minutes.
The Tigers started the second half firmly on the front foot with centre Ollie Smith ruled not to have touched down over the line by the television match official.
However, the pressure was unrelenting and – after nine minutes of solid defending – the visitors finally buckled.
When Dan Hipkiss was held on the line after a powerful surge, Hamilton was on his shoulder to touch down.
Goode’s conversion was ruled successful although the ball had drifted wide and the same player added another penalty to take the score to 16-9 as the hour approached.
The Falcons struggled to get a foothold in the game but their determination was rewarded after a long passage of play saw lock Geoff Parling break down the right and the ball was spread to the opposite wing and Morris touched down in the corner, with Burke converting from close to the left touchline.
The Falcons’ full-back missed a penalty attempt from just inside the Tigers’ half in injury time and, while this was a major improvement on last season’s 83-10 defeat at Welford Road, Newcastle will believe they deserved more.