Ipswich leap-frogged Cardiff into second place after a Jason Scotland strike and an Adam Matthews own goal sealed the win for the Tractor Boys.
The visitors were on top in the opening exchanges, but Roy Keane's side took a stranglehold midway through the first-half that they did not surrender.
Matthews sent a powerful header into his own net from Carlos Edwards' cross in the 62nd minute at Portman Road.
And striker Scotland produced a low shot finish following a break-out.
After Keane's side got into their stride, the Bluebirds, without injured skipper Craig Bellamy, were regularly under pressure, particularly whenever Connor Wickham was anywhere near the ball.
The 17-year-old was making his first appearance of the season and his battle with Cardiff defender Gabor Gyepes was one of the game's combative highlights.
The Ipswich man was yellow-carded for a late, clumsy first-half challenge on Lee Naylor and he risked a second after the break by bringing Gyepes down.
But as Wickham gradually got the better of his man, so the hosts took an increasing grip on the game.
Gareth McCauley's flicked on header bounced harmlessly past David Marshall's far post and as Ipswich's pressure increased, Wickham created a great chance, but was unable to capitalise on the rebound.
Marshall pulled off a brilliant save after Wickham proved too strong for Gyepes and Mark Hudson, the keeper pushing the shot off the floor and over the bar.
But despite all of Ipswich's Wickham-inspired efforts and Cardiff's resolute defence, the opening goal was stylish if unfortunate for 18-year-old Matthews.
Trinidad and Tobago midfielder Carlos Edwards sent what seemed a harmless cross into the Cardiff box and Matthews met it with a header timed to perfection for the own goal.
Peter Whittingham found his path blocked as Cardiff upped their efforts and Jay Bothroyd was also denied before ex-Swansea City player Scotland finished off a break-out with a well-taken, low drive from close range.
Marton Fulop got a hand to a Whittingham header as Cardiff sought an immediate response and Chris Burke fired over the top in time added on.
Manager Roy Keane was delighted with the newly signed Trinidad striker added that Jason Scotland adds a new dimension to the Ipswich attack.
Jones goal denies West Ham a victory.
By Paul Fletcher (BBC Sports).
West Ham picked up their first point of the Premier League season with a hard-fought draw against Stoke.
Scott Parker put the visiting side in front with a close-range finish after Stoke failed to clear a free-kick.
Kenwyne Jones equalised with a header and had a strike tipped on to the post by Robert Green, while Robert Huth and Ricardo Fuller also hit the woodwork.
West Ham struck the post through Frederic Piquionne, while Thomas Sorensen denied Manuel da Costa.
It was a tough and uncompromising contest between two teams who started the day in the bottom three.
The result ensured that the Hammers, without boss Avram Grant as he observed the Jewish holy day Yom Kippur, remained anchored to the bottom of the table but they have at least ended their sequence of four straight defeats, during which they conceded three goals in each.
Referee Lee Mason dished out five yellow cards, but turned down several penalties appeals, with West Ham furious that Ryan Shawcross was not punished for a handball following a Victor Obinna strike in the opening half.
A foul from Shawcross led to West Ham's goal, with Stoke failing to deal with Obinna's subsequent delivery into the box.
Delap attempted to hack the ball clear but it struck team-mate Shawcross and was bundled home by Parker.
The goal came just after the half-hour mark and Piquionne almost immediately doubled their advantage with a long-range shot that thundered against the crossbar.
Shawcross was later fortunate to escape sanction when he appeared to elbow Carlton Cole in an off-the-ball incident that saw the striker fall to the turf.
Stoke, who defeated Aston Villa with a last-ditch winner on Monday, looked strangely off the pace but were almost handed a goal by the unsure handling of Green.
The Hammers keeper fumbled a delivery from out wide and Huth almost tucked the ball home from a tight angle but the defender's shot struck the post.
Jones should then have converted a long throw from Delap but he too was wasteful, heading over from six yards.
However, the former Sunderland striker was on target shortly after the restart, rising above Da Costa, making his appearance start of the season, to convert a brilliant cross from the right by Jermaine Pennant.
The goal brought the crowd to life and they were almost celebrating again when the athletic Jones dispossessed Matthew Upson before cutting inside and unleashing a fearsome shot that Green diverted against the woodwork with a superb one-handed save.
West Ham responded, with a neat interchange of play creating an opening for Obinna but Thomas Sorensen palmed his long-range effort around the post and brilliantly denied a Da Costa header from the subsequent corner.
The last effort of the match fell to former Hammer Matthew Etherington, whose long-range effort with the outside of his boot was saved by Green.