Goals from Jay Rodriguez and Harvey Barnes lifted West Bromwich into second place and left Ipswich still five points adrift at the bottom of the Championship table.
The Baggies climbed above Middlesbrough, Leeds and Sheffield United thanks to a victory that should have been by a far more comfortable margin.
Ipswich worked hard under new manager Paul Lambert, who had previously presided over two draws, and were given brief hope of an unlikely comeback when Tosin Adarabioyo's error allowed substitute Kayden Jackson to pull one back with five minutes remaining.
Rodriguez opened the scoring in the 26th minute by tapping in a header across the box from left-back Kieran Gibbs who had met a cross to the back post by Matt Phillips.
'I didn't realise it was my 100th goal but I'm more annoyed that I missed a couple of chances to kill off the game,' the striker said.
'We're still disappointed at times with some of the things we do but we're a work in progress. There is more to come from us.'
Ipswich, easy meat under previous boss Paul Hurst, were more of a force after the break but were relieved when Barnes hit a post rather than the back of the net before the hour mark.
The on-loan Leicester man doubled the lead with a 77th-minute second by cutting in from the right of the box and lashing past Bialkowski.
That should have been that but Adarabioyo's dreadful touch in his own box allowed Jackson a simple finish with five minutes to set up a nervy finish.
Teenage substitute Jack Lankester grazed a post with a stoppage-time free-kick and Albion were releived to hear the final whistle soon after.
'On another day we might have got an equaliser and I said to them in there sometimes the table DOES lie,' said Lambert, who had begun his stint as Hurst's successor with two draws..
'We gave everything, we couldn't give any more. I can't predict what's going to happen with results but one thing for sure is we're certainly a good side.'
Baggies boss Darren Moore had words of comfort for 21-year-old right-back Adarabioyo, who is on loan from Manchester City.
'He had a tremendous game, young Tosin, and he will learn from it,' he said. 'He knows, in terms of his career development, this will be a valuable lesson for him.'
