Arsenal, who fielded 41-year-old German Jens Lehmann in goal for the first time in three years as an emergency stand-in for Manuel Almunia, were 2-0 up after 21 minutes thanks to well-worked goals from Abou Diaby and Emmanuel Eboue.
Blackpool replied after 52 minutes when Gary Taylor-Fletcher scored after referee Lee Mason waved play on despite Lehmann bringing down DJ Campbell in the penalty area.
Although they had other chances, including a strong appeal for a penalty when Laurent Koscielny appeared to bring down Taylor-Fletcher, the seaside strugglers failed to find the equaliser which could have eased their increasing relegation worries.
Instead, Arsenal wrapped up the victory with a superb counter-attacking goal after 76 minutes when Cesc Fabregas and Theo Walcott combined on the break before Walcott crossed for Robin Van Persie to score in front of goal.
In the day's other match Aston Villa ended their recent run of poor form with a first win in four matches, beating Newcastle United 1-0 thanks to a first half header from James Collins at Villa Park.
The win saw Villa climb from 16th to 14th while Newcastle remain ninth.
Lehmann, who left Arsenal three years ago and returned after coming out of retirement last month to help solve a goalkeeper crisis, was called into the game just before kickoff after Almunia injured his knee in the warm-up.
The result lifted Arsenal to 62 points - seven behind United with a game in hand. Blackpool remained a point and a place above the relegation zone but after a bright start to the season they have now lost 11 of their last 15 league games.
Despite their failures in the Champions League, the FA Cup and the League Cup, Arsenal have been unbeaten in the Premier League for nearly four months and there appeared little chance of them losing on Sunday after scoring their early goals.
"We were in control in the first half, but had a nervy moment in the second half at 2-1, but fortunatly we got the third goal and from then on it looked quite comfortable," Wenger told the BBC.
The Frenchman admitted that when he re-signed Lehmann he did not really expect him to play.
"Not really no," he said, "but Jens is a competitor and has worked very hard in training and has improved in the last three weeks and I am very happy for him."
Of their chances of overhauling United, Wenger said Arsenal were still in the very much in the hunt.
"We are on a long unbeaten run, and lets hope we can put wins together."
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