Roadway intersections are among the major causes of traffic congestion besides lane reduction bottlenecks. When a major road intersects a minor road at an unsignalized intersection without the control of a traffic signal, the mainline vehicles are given priority over the minor road vehicles to go through the intersection, and the latter can only enter or cross the intersection when there is a sufficient gap between successive vehicles on the major road. Connected and automated vehicles (CAV) are packed with tracking and lane-keeping assistance and adaptive speed control to ensure that vehicles do not collide while reducing traffic congestion. This research aims to utilize CAVs to help generate usable gaps for minor road vehicles to enter the intersection without interrupting the mainline traffic flow. A probability function is developed to study the probability in which CAVs can create additional usable gaps for the minor road vehicles based on the headway distribution of the mainline vehicles. The control logic algorithm is utilized when vehicle arrivals on the main road permit implementing the control strategy to improve intersection efficiency in mixed traffic conditions. The proposed control logic is simulated under two traffic scenarios, unsignalized and semi-actuated signal control, to study the effectiveness of the proposed method. Additionally, a field investigation is conducted at two intersections to verify the feasibility of the control logic implementation in real traffic conditions. Simulation results of the unsignalized intersection scenario show that the delay and queue length of the minor road approach is minimized without causing a significant delay to the mainline. The minor road delay is reduced by as much as 90% when the percentage of CAVs on the major road is 70% compared with the benchmark of no CAVs on the major road. The modified algorithm of semi-actuated signal control reduces the major road interruptions with the increase of CAVs penetration. Additionally, the intersection capacity increases with the increase of the number of gaps created on the major road. The minor road drivers are mostly willing to accept gaps created when CAVs reduce speed, where more than 60% of gaps created were accepted. This research has shown that deploying CAVs in the road network with the proposed method can positively impact the traffic efficiency while maintaining safety of the intersection.