Chelsea won 2-0 at Portsmouth on Tuesday to go eight points clear with 49 points from 20 matches. Arsenal reduced the gap to five points taking their tally to 44 points from 20 games.
Manchester United, who won 1-0 at Aston Villa on Tuesday are third on 40 points with Everton, 2-0 losers at Charlton, also on 40 points in fourth place.
Arsenal wrapped up their third successive league win with Vieira scoring in stoppage time at the end of the first half after reacting first to a loose, bouncing ball.
His 20-metre volley which took a slight deflection, gave goalkeeper Shay Given no chance in the United goal and despite some spirited attacks, Newcastle failed to score and have now gone six games without a league win.
"It was a fantastic team performance" Vieira told Sky Sports News. "If we keep playing like that and get results like that we will be there or thereabouts at the end of the season."
LATE GOALS
On Tuesday Chelsea required late goals from Dutchman Arjen Robben and Joe Cole to earn a 2-0 win at Portsmouth while resurgent Manchester United beat Aston Villa 1-0 to register their seventh win in eight league games and move to third.
Middlesbrough beat Norwich City 2-0 with goals from Cameroon striker Joseph-Desire Job to stay fifth on 35 points, one ahead of Liverpool, who edged Southampton 1-0 with a winner from French forward Florent Sinama-Pongolle.
Everton suffered their first league defeat for nearly two months in a pulsating final eight minutes at Charlton, conceding two goals and having Scottish striker Duncan Ferguson sent off.
Birmingham City won 3-2 at Fulham and Blackburn Rovers moved further away from the drop zone with a 1-0 win at struggling Bolton Wanderers, who have now lost six on the trot.
Tottenham Hotspur were denied a sixth consecutive league win by Andrew Johnson in a 1-1 draw with Crystal Palace, while an 85th-minute own goal by Manchester City defender Richard Dunne cost them a 1-1 draw with 10-man West Bromwich Albion.
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