Wellens had already been booked after 17 minutes for a misdemeanour on Alan Smith.
The closest the Magpies came to capitalising on their numerical advantage was when Patrick Van Aanholt forced a save from Chris Weale late in the first half.
The point extended Newcastle's unbeaten league run to 14 matches and saw Chris Hughton's side stretch their lead at the top of the table to four points after nearest rivals Nottingham Forest were beaten 1-0 at Pride Park by Derby earlier in the day.
Steve Harper tipped a shot from Matty Fryatt over the crossbar midway through the first half, while at the other end Weale pushed Van Aanholt's effort round a post.
The Magpies twice went close in quick succession from corners courtesy of headers from Smith and Andrew Carroll.
Kevin Nolan threatened with another headed effort at the start of the second half.
A rare Leicester attack saw on-loan Sunderland striker Martyn Waghorn fire a left-foot shot just wide soon afterwards.
Carroll saw a goalbound effort blocked by Wayne Brown with 10 minutes remaining.
There was a notable moment six minutes from time when Leicester's new signing Nolberto Solano came on as a substitute for his debut.
The Peruvian received a warm reception from both sets of supporters having spent eight years at Newcastle during spells between 1998 to 2004 and 2005 to 2007.
The Magpies continued to push forward and came close to a winning goal in the final minute but Routledge's shot cleared the crossbar.
Newcastle remain unbeaten in the league since losing 2-1 at Scunthorpe on October 20 while Leicester's play-off hopes continue to stutter - the Foxes are without a win in their last four matches.