And with 13 minutes left, Edgar Davids fired in number two - his first in the Premiership - to wrap up the points and give Spurs their first win in five games.
But Wigan set-up a nail-biting finish by pulling one back two minutes from time. Henri Camara's cross was parried by Paul Robinson but it ran to the unmarked Lee McCulloch who made no mistake slotting it home at the back post.
Paul Jewell had the luxury of a fully-fit squad available and opted to make a surprise change to the side beaten by Arsenal in last week's five-goal thriller - a result that ended a run of six straight Premiership wins.
Experienced keeper John Filan, who was criticised over the first of the Gunners' goals, got a vote of confidence during the week but he was still left out, dropped for the first time since joining Wigan from Blackburn four years ago.
It meant another chance for ex-Rotherham keeper Mike Pollitt, who was in the side at the start of the season when Filan, 35, was recovering from a hernia operation.
For Jol it was a landmark occasion, his 50th game in charge, and Spurs were looking to end a run of four matches without a win.
He stuck with Keane up front in partnership with Egyptian striker Mido and Jermain Defoe on the bench.
Despite making his return in the reserves in midweek after a foot injury, there was no place for Wayne Routledge, deemed not to be quite ready for first-team action.
Wigan were quick out of the traps, forcing two early corners and almost cashing in on a disastrous clearance by keeper Robinson.
It went straight to midfield general Jimmy Bullard, who sent Jason Roberts racing in on goal. But Spurs skipper Ledley King was quick to spot the danger, and got back to spare the England keeper further embarrassment.
Republic of Ireland international Graham Kavanagh fired just wide from long range as Wigan kept up the momentum.
But manager Jol's decision to stick with Irish star Keane up front was justified as Spurs grabbed the lead.
Teemu Tainio provided a deep ball which de Zeeuw inexplicably failed to cut out. It gave Keane a chance he gratefully snapped up, rounding Pollitt before sliding the ball into an empty net.
Typically the Latics went in search of an equaliser with McCulloch heading over from a Bullard corner and Camara miscuing in front of goal.
But it required a timely tackle from Wigan right-back Pascal Chimbonda to deny Mido the chance of a second for Spurs.
Kavanagh let fly with another fierce left-foot strike but again failed to hit the target, while goalscorer Keane was proving a handful for the Wigan defence at the other end.
He protested to referee Mike Riley after Swiss defender Stephane Henchoz appeared to hold him back inside the area, but the official waved aside his claims for a penalty.
King did well to hold off Camara as he headed into the Spurs box and Kavanagh almost made it third time lucky - this time hammering just wide with his right foot.
England Under-21's left-back Leighton Baines almost registered his first goal for almost a year, but his left-foot strike deflected off McCulloch's head and the touch was enough to take it off target.
Jermaine Jenas tried his luck from long-range with a free-kick before Wigan struck on the break with McCulloch supplying the long ball from the speedy Camara to chase. But Robinson reacted to the danger, nipping out of his area to head it clear before the Wigan striker could get to it.
Spurs were agonisingly close to snatching a second when the unmarked Finnish star Tainio lashed in a shot from the left, but Pollitt came up with a diving save to keep it out.
Jewell signalled Wigan's intentions to make a fight of it when he sent on Irish forward David Connolly for midfielder Damien Francis and left three up front.
But it left the Latics vulnerable to the counter attack and it led to Spurs' second, as the defence backed off Davids and he beat Pollitt with a drive into the far corner.
McCulloch got one back and Spurs had to survive four minutes of stoppage-time before they could start celebrating.
Man of the Match: Teemu Tainio
An energetic performance from the Finnish midfielder, who set up the first goal and almost got one himself in the second half.