A 25-yard free-kick from Willo Flood was enough for the Blues to keep the pressure on United's second string at the top of the table.
The only goal of the game came after just 35 seconds when Flood's delivery flew over the head of veteran Bolton keeper Kevin Poole.
City could even have gone two ahead seconds later but striker Karl Bermingham, who made two substitute appearances on loan at Lincoln earlier this year, dragged his shot wide.
Bradley Wright-Phillips led the City attack and was denied by the legs of Poole before the break.
Early in the second period, Bolton's Khalilou Fadiga struck the top of the City crossbar with a well-struck free kick, while Bermingham spurned another chance.
With 74 minutes gone, City youngster Danny Sturridge was introduced. Aged just 15, he has been the subject of speculation in the national press recently, linking him with a move to Chelsea.
In the closing stages Poole denied Ireland, before Bolton’s Radhi Jaidi somehow sent a downwards over the bar.
City keeper Geert De Vlieger managed 90 minutes as he stepped up his recovery from an Achilles injury which has sidelined him since last August.
City: De Vlieger, Warrender, Collins, J D’Laryea, Sommeil (Lee-Matthews 76), Richards, Flood, Ireland, B Wright-Phillips (Sturridge 74), Bermingham, Croft (Miller 90). Subs: Ellegaard (GK), Bennett.
Bolton: Poole, Kribib (Talbot 68), Cesar, Laville (Powell 23), Jaidi, Campo, O’Brien, Kaku, Pedersen, Buval, Fadiga. Subs: Ashton (GK), Whitehead, Sinclair.