In a drab first half, Ryan Shotton's drive was deflected on to a post and Jon Walters twice went close.
Dean Whitehead opened the scoring shortly after the break with a low finish and substitute Peter Crouch sealed the win with a tap-in.
Roberto Colautti headed home late on but Stoke held on for the three points.
The result sees the Potters move on to 10 points, four clear of second-placed Besiktas, with two games remaining in Group E.
A point against Dynamo Kiev at the Britannia Stadium on 1 December would secure their place in the last 32.
With this the second of three games in seven days for Stoke, it was hardly surprising to see nine changes from the side that started against Newcastle in the Premier League on Monday.
But it was still a team that included the likes of Robert Huth, Wilson Palacios and Kenwyne Jones as Stoke looked to extend their unbeaten run in Europe to 10 matches.
Huth headed wide inside two minutes, Andy Wilkinson blasted over from Shotton's cut-back and Jones was squeezed out when bearing down on goal.
The hosts had not lost in 12 home European games but looked shaky at the back and bereft of attacking ideas, inviting Stoke forward for further opportunities.
Shotton's low strike was deflected on to the post by Matthew Upson and an unmarked Walters headed straight at 18-year-old goalkeeper Barak Levy.
Uri Cohen volleyed wide at the end of a rare Maccabi foray into opposition territory, but that was the visitors' only moment of slight concern all half.
They might have taken the lead on 43 minutes when Jones flicked a long Thomas Sorensen kick into the path of Walters, only for an offside decision to rule the effort out.
Maccabi would have been out of contention were it not for Stoke's profligacy, but their fortune eventually ran out as the visitors opened the scoring.
Salif Diao and Wilkinson worked possession to Walters, who nudged Savo Pavicevic out of the way, allowing Whitehead to take a touch and finish low past Levy.
It was no more than Stoke deserved and with Maccabi offering next to nothing in the way of a response, the lead was soon doubled.
Pulis introduced Crouch for Walters and with his first touch the 6ft 7in striker tapped in Whitehead's cross after good work from Jones.
Another substitute, Colautti, forced a tense finale with an excellent header from Sheran Yein's cross, but Stoke defended well to collect a deserved win.