Gutierrez opened the scoring with 12 minutes gone when his shot was deflected home by defender Ian Evatt, and further goals from Andy Carroll, Kevin Nolan and Wayne Routledge maintained the Magpies' six-point advantage over second-placed West Brom.
Victory at Reading on Tuesday evening would leave Chris Hughton's men needing a single point from their final three games to claim the trophy.
Blackpool, one of only four sides to beat Newcastle in the league this season, gave as good as they got for long periods in front of a crowd of 47,010, but crucially, they were unable to convert pressure into clear-cut chances until it was too late.
By contrast, Newcastle were clinical in front of goal and had it not been for the woodwork and the excellence of keeper Matt Gilks, they might have won even more handsomely.
The Magpies took the lead with 12 minutes gone when Gutierrez ran on to Tamas Kadar's pass and tricked his way past Seamus Coleman and Alex Baptiste before charging into the box and firing past Gilks with the help of a deflection off Evatt.
Gutierrez celebrated by donning his Spiderman mask, but his joy might have been short-lived had DJ Campbell not stabbed a weak shot straight at Harper from Charlie Adam's 18th-minute through-ball.
The South American tested Gilks from distance seconds later and the keeper had to collect Carroll's 25th-minute header, although he did so with little difficulty.
Blackpool continued to enjoy sustained periods of possession, but without hurting Newcastle unduly, and the home side increased their lead nine minutes before the break when Carroll met Danny Guthrie's free-kick with a deft header to beat Gilks.
The second half got underway in scrappy fashion with both sides struggling to retain possession, although Gilks had to make a good save to keep out substitute Ryan Taylor's 49th-minute free-kick.
Carroll headed wide from the resulting corner, but the Blackpool keeper needed the help of the post to keep out Peter Lovenkrands' 52nd-minute effort.
Gilks had to make a double save from Gutierrez and Lovenkrands three minutes later as Newcastle turned the screw, and he pulled off a stunning 59th-minute stop to keep out the Dane's header.
But there was nothing he could do to deny Nolan three minutes later as he ran on to Gutierrez's pass and nonchalantly walked the ball past the keeper and into the net.
It should have been four with 18 minutes remaining, but Lovenkrands blazed over after being set up by Gutierrez and Carroll.
However, the home fans did not have to wait long for Wayne Routledge to burst into the penalty area and fire low into the far corner 13 minutes from time, and substitute Brett Ormerod's 85th-minute strike proved little consolation.