Ghana sealed top spot in Africa Cup of Nations Group B and a quarter-final meeting with Cape Verde by outclassing Niger in Port Elizabeth.
The World Cup quarter-finalists were simply too strong for opponents who finished bottom of the pool and might have enjoyed an even more emphatic win.
Asamoah Gyan set the Black Stars on their way and Christian Atsu added a second before the break. John Boye ended any faint hopes of a Niger comeback with the third soon after the break.
Niger, who needed a win to have any chase of progression, could look to one moment as a possible turning point, when they scored what they thought was an equaliser only to have it disallowed, but in truth they were dominated from the outset.
The Black Stars went in front after six minutes when Albert Adomah's ball in front the right was controlled with one touch Gyan, who then lashed home a low finish with his second.
Niger almost got an instant equaliser but their goal was disallowed with Moussa Maazou penalised, somewhat harshly, for a foul on goalkeeper Fatau Dauda.
The underdogs chanced their arm again when Mohammed Chicoto went for the spectacular, with his overhead attempt sailing over.
But it was at the back where they had problems and they fell further behind in the 23rd minute.
Gyan this time turned provider and his left-wing cross was controlled by the chest and then skilfully knocked in by Atsu at the back post.
Ghana almost had a third before the break only for Kassaly Daouda to superbly parry Emmanuel Agyemang-Badu's drilled shot.
Instead number three came just four minutes after half-time. Gyan's header was saved, but Boye, sporting a peroxide cross in his hair, was the quickest to react and tapped home the rebound from barely a yard.
Niger had no answer to their opponents' far superior ability, and they would have conceded again had Gyan not contrived to send a half-volley wide when it seemed easier to score. It was never going to prove costly, though, as Ghana coasted to a comfortable win.
Sky Sports understands Graham is eager to return his native north east and has been heavily linked with a move to Sunderland.
Swans boss Michael Laudrup confirmed that the club had received an offer for the 27-year-old, but hinted that it did not meet their valuation.
Norwich are also reportedly interested in the striker, who has scored seven goals in 22 appearances this season.
Despite his desire to leave, Laudrup said that Graham could remain at the Liberty Stadium beyond the current transfer window.
He said: "If he comes and says he wants to leave and there's a very good offer we'll have to look into it.
"It could easily happen that we have exactly the same squad in February as we have now."
Graham has been included in Swansea's squad for Tuesday's Premier League trip to Sunderland.
