They never allowed Arsenal to run away with it, while Gunners keeper David Raya was forced to keep out Ross Barkley's free-kick on the stroke ofhalf-time.
The only thing to spoil their evening was an injury to captain John Terry that saw the centre-half limp off before half-time and leave him as a doubt for Tuesday's trip to play Paris St-Germain in the first leg of their last-16 Champions League
The Super Eagles were less relentless in attack even with the presence of Zambia president Edgar Lungu, as the trio of Iwobi, Iheanacho and Moses Simon gave Stopilla Sunzu's marshaled backline a torrid time.
The Belgium midfielder did not make it on to the pitch this time, but the sight of him warming up on the touchline in the second half brought huge cheers from the home fans.
The visitors went ahead just before half-time when Gomes was left unmarked eight yards out and rose well to powerfully head home Pablo Sarabia's right-wing corner. But Tottenham made it 1-1 after only 34 seconds ofthe second half.
It set the platform for a second halfof total Chelsea domination that was nevertheless laced with anxiety as the hosts missed chance after chance to put the game to bed.
Musa showed superb technique to fire Nigeria ahead on thehalf-volley before the Leicester player rounded keeper Hannes Thor Halldorsson to make it 2-0.
It was a superb finish by the England forward, controlling a low ball from the right before striking into the bottom-right corner from the edge ofthe area.
Diego Costa made it 3-0 from a corner just before half-time and Hazard scored the pick ofthe goals after the break. Pedro put the gloss on the result when he tapped into an empty net.
It was the striker's fifth goal in his last three matches, while the penalty was Bournemouth's first in 65 games, ending a stretch of 609 days without a spot-kick.
The hosts are already through to the Germany tournament but did not take things easy as Kylian Mbappe hit a hat-trick that included a 40-yard strike. Teenager Warren Zaire-Emery was one of seven different first-half scorers.
The Three Lions captain, who received treatment on a knee injury in the second half but was able to continue, is six short of Lewandowski's record of 41 goals in a Bundesliga season with three games left.
United have started to string a run of form together with the 2-1 win over Sheffield United and they made it three consecutive wins with a narrow victory over the Danish champions thanks to a second-half goal from Harry Maguire.