Williams thundered a volley home from the edge of the box in first-half stoppage time and, although it may have been harsh on Leeds at the time, by the end Town were worthy winners.
Leeds skipper Kevin Nicholls spoiled a successful comeback from injury when he stupidly lashed out at Danny Haynes a minute after being cautioned and was red carded by referee Keith Stroud.
The visitors didn't threaten for much of the game, although for long spells of the first half Ipswich looked equally insipid in the first match at Portman Road since the five murders of prostitutes who had been working near the club's ground.
The match was preceded by a prayer by Bishop of St Edmundsbury and Ipswich, the Rt Reverend Richard Lewis and a minute's silence, and the game took a long time to get going.
An early Williams corner flew dangerously across the six-yard line before Tresor Kandol had the ball in the Ipswich net, but the flag was up for offside when he collected Jonathan Douglas' pass.
Sylvain Legwinski fired in the first shot on target on 25 minutes after a one-two with Jon Macken, but it was straight at Graham Stack.
Owen Garvan produced a fine tackle to deny former Blue Ian Westlake a shot after Douglas laid off an Ian Moore cross, but it was a rare Leeds threat.
Nicholls sent a 25-yard free-kick well wide before Alex Bruce cleared when Lewis Price spilled a high Douglas cross with Kandol waiting to pounce.
Kandol wasted Leeds' best chance of the half when, appearing offside, he controlled a Douglas cross and poked a shot narrowly wide of goal as Richard Naylor got back to pressure him.
Gary Roberts sent a chip onto the roof of the net and Price saved Kandol's looping header before Williams struck as he collected an Alan Lee knockdown, took a touch inside Hayden Foxe and lashed a 20-yard dipping shot over the helpless Stack.
Leeds made a promising start to the second half, without creating anything much, before Roberts and Williams fired in efforts off target and the former also saw an angled shot gathered by Stack.
Stack had to dive to hold a 16-yard Lee shot after Macken fed him before Kandol headed wide after Price could only punch a curling Nicholls free-kick straight into the air.
Price dived to palm away Kandol's goalbound prod from a Moore lay-off before sub Seb Carole forced Price into a save on his near post from a 20-yard strike.
Carole had a better chance when he escaped down the left flank moments later, but with colleagues screaming for a pass inside, he shot from a tight angle and Price parried it away.
Nicholls then lost his head a minute after being cautioned for kicking out at Lee when he clattered into Haynes with a raised arm and, after a spell of pushing and shoving, ref Stroud showed a straight red card.
Matt Heath headed an Eddie Lewis free-kick wide as the ten men still tried to press for an equaliser, but they left themselves open to a counter, although Town failed to kill the visitors off.
The game ended with the fifth and sixth yellows of an increasingly niggly game - Naylor cautioned for a high challenge on Kandol and then sub David Healy booked for hacking down Roberts.
Town hung on to claim only their third clean sheet of the season and open up a nine-point gap on the fallen giants who look to stay in the bottom three for Christmas.