Simpson scored two and set up two as the hosts won for only the second time at home in the league this season.
The Lions got off to a flyer against a shellshocked Ipswich side with two goals in the opening nine minutes.
Excellent work from Liam Feeney created the opener after five minutes, the midfielder beating a defender then checking back on to his weaker left foot to delivery a cross for Simpson.
Simpson's initial shot was saved by David Stockdale, as was Darius Henderson's follow-up attempt, before the Hull loanee slotted in from six yards.
Barely four minutes later, a marauding Liam Trotter forced Ibrahima Sonko to back up and picked out Simpson racing on the outside.
This time the former Arsenal trainee's shot was again stopped by Stockdale, but Henderson was quickest to react once more and drive the ball home for his fourth goal in two games.
The Blues had been on a run of six games without defeat before last week's loss against Crystal Palace, and their recovery task was made all the more difficult when the experienced Lee Bowyer limped off after 17 minutes.
A lacklustre Ipswich could have reduced the deficit on the half-hour when Jason Scotland broke free but his shot past the onrushing David Forde was well wide.
And the day got worse for Paul Jewell five minutes before the interval when Sonko limped off with a groin injury to be replaced by Ivar Ingimarsson.
Brian Howard had a chance moments later to rub salt in the gaping Ipswich wound - his powerful left-footed drive skewing narrowly wide.
Kenny Jackett's men won for the first time in 11 league games last time out at Leicester and could have made sure of the points as early as the 57th minute.
Simpson was again at the centre of play, this time his effort coming back off the post to Howard, whose shot was kept out by Stockdale despite claims the ball crossed the line.
But the 1600 away fans finally had something to cheer after 65 minutes when Scotland fed Jimmy Bullard who sidefooted the ball past Forde to reduce the deficit.
Their excitement lasted only seven minutes when two goals in two minutes sealed the victory for the hosts.
Unsurprisingly, it was Simpson who picked out Feeney to slot under the goalkeeper for his first goal at The Den.
And Simpson added the final touch with a clever finish in the 75th minute, cutting inside a defender and drilling a low shot into the corner.