The game had been in doubt ahead of kickoff, with thick fog restricting visibility at the City Ground, but referee David Webb decided that the match could go ahead.
The visitors thought that they had won a penalty in the first half, when Lee Martin appeared to be fouled inside the area, but the referee waved their appeals away.
However, Martin was sent off later in the first half for violent conduct, having brought down Henri Lansbury.
Ipswich defended well early in the second half, as Forest tried to make the most of their numerical advantage.
An unfair challenge from Richard Stearman, who had been booked in the first half, saw the referee reach for another yellow card, reducing the Tractor Boys to nine men with over 20 minutes left to play.
Simon Cox managed to put the ball in the back of the net inside the final 10 minutes for the hosts, but the striker was judged to have been offside.
The visitors continued to defend strongly, forcing Forest to try their luck from distance, eventually resulting in Lewis McGugan taking a shot from 25 yards that took a big deflection to beat Stephen Henderson in the Ipswich goal and give Forest all three points late on.
The win lists Forest up to seventh in the table, while Ipswich remain 19th.